Cubes And Cube Roots Questions

We provide cubes and cube roots practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on cubes and cube roots skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

Cubes And Cube Roots Questions

List of cubes and cube roots Questions

Question No Questions Class
1 Examine if 398 is a perfect cube. If not,
then find the smallest number that
must be subtracted from 398 to obtain
a perfect cube
8
2 127
343 is equal to
13
(3) 9
(2) 1-2
(41-2
8
3 The cube root of 4.096 is
A . 1.6
B. 1.7
( c cdot 1.8 )
D. 2.6
8
4 Find the cube root of 614125 using
prime factorization:
A . 65
B. 75
c. 85
D. 95
8
5 Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:
A .243
в. 3072
c. 11979
D. 19652
8
6 Estimate the value of cube root of the
number 1333
A . 10.99
B. 20.10
c. 12.45
D. 10.56
8
7 Represent the number 19 as the
difference between the cubes of natural
numbers.
8
8 If ( boldsymbol{alpha}=mathbf{3}, boldsymbol{beta}=mathbf{5} ) and ( gamma=mathbf{8}, ) then the
value of ( boldsymbol{alpha}^{3}+boldsymbol{beta}^{3}+boldsymbol{gamma}^{3} ) is
A. -240
в. 240
c. -360
D.
8
9 The cube of a two digit number may be a three digit number.
A. True
B. False
c. Insufficient Data
D. None of these
8
10 Find the digit at unit’s place of ( 128^{3} )
( A cdot 8 )
B. 6
( c cdot 4 )
D. 2
8
11 Find the cubes of the following
numbers:
40
8
12 A perfect cube does not end with two
zeros
A. True
B. False
c. Ambiguous
D. Data insufficient
8
13 Cubes of Negative integers are negative
A. True
B. False
c. Ambiguous
D. Data insufficient
8
14 Find the cube root of
( 99-70 sqrt{2} )
8
15 Find the smallest number that must be
added to 400 to make it a perfect cube
A . 108
в. 112
c. 18
D. 12
8
16 The cube of a two digit number may have seven or more digits.
A. True
B. False
c. Insufficient Data
D. None of these
8
17 If the volume of a cuboid is ( 3 x^{2}-27 )
then its possible dimensions are
A. ( 3, x^{2},-27 x )
в. ( 3, x-3, x+3 )
c. ( 3, x^{2}, 27 x )
D. 3,3,3
8
18 If ( omega ) is an imaginary cube root of unity
then ( left(1+omega-omega^{2}right)^{7} ) equals?
A. ( 128 omega )
B. ( -128 omega )
c. ( -128 omega^{2} )
D. None of these
8
19 Write the units digit of the cube for 109
( A cdot 1 )
B. 7
( c .9 )
D. 3
8
20 The value of ( (27 times 2744)^{frac{1}{3}} ) is
A . 40
B. 42
c. 22
D. 32
8
21 Find the smallest number by which a
given number must be multiplied to obtain a perfect cube 72
8
22 Find the value of ( (47)^{3} ) using the shortcut or column method 8
23 Find the smallest number by which a given number must be divided to obtain
a perfect cube 704
8
24 Find the nearest integer to the cube root
of 331776:
8
25 Evaluate the following:
( mathbf{1 0 4}^{mathbf{3}}+mathbf{9 6}^{mathbf{3}} )
8
26 Find the cube root of 39304 by estimation method.
A . 24
B. 44
( c .34 )
D. 54
8
27 Evaluate the following:
( 46^{3}+34^{3} )
8
28 64. 553 + 173 – 723 + 201960 is
equal to
(1)-1
(2) O
(3) 1
(4) 17
8
29 Find the smallest number by which a given number must be divided to obtain
a perfect cube
81
8
30 What is the smallest number by which
3645 be multiplied so that the product becomes a perfect cube?
A . 5
B . 25
c. 15
D. 35 5
8
31 Cube of 1.5 is:
( mathbf{A} cdot 3.375 )
B. 33.75
c. 3.125
D. 31.25
8
32 How many consecutive odd numbers are required to form ( 10^{3} ) as their sum?
A . 10
B. 11
( c .9 )
D. 20
8
33 The smallest number by which 392 must be multiplied so that the product is a perfect cube, is
A . 3
B. 5
( c cdot 7 )
D. 9
8
34 Find the smallest number which should be multiplied to 231525 to make it a
perfect cube.
A . 5
B. 3
( c cdot 7 )
D. 21
8
35 The prime factor of 128 is
A. 0
B. 1
( c cdot 2 )
D. 3
8
36 ( ln (34)^{33} ) unit digit is 4 8
37 If ( 27=a^{3}, ) find the value of ( a )
( mathbf{A} cdot mathbf{1} )
B . 2
( c .3 )
D. 4
8
38 If cube of ( 1 frac{2}{3}, ) is of the form ( frac{a}{b}, ) then ( a+ )
( b ) is equal to:
8
39 Find the cube root of each of the
following numbers by prime factorisation method:
13824
A . 14
B . 24
( c .34 )
D. 44
8
40 What is the least number which must
be subtracted from 369 to make it a
perfect cube?
( mathbf{A} cdot mathbf{8} )
B . 26
( c cdot 2 )
D. 25
8
41 The smallest number by which 8,788 must be divided so that the quotient is
perfect cube is:
( A cdot 4 )
B. 12
( c cdot 16 )
D. 32
8
42 Find the cube root of :
8
8
43 Find the smallest number which should
be multiplied to 100 to get a perfect
cube.
8
44 Which of the following numbers are perfect cubes? In case of perfect cube find the number with cube is the given number.
( mathbf{2 1 9 5 2} )
8
45 The cube root of any multiple of 8 is always divisible by:
A . 2
B. 4
c. 8
D. 16
8
46 Cube of any odd number is even
A. True
B. False
c. Depends on the number
D. Data Insufficient
8
47 The value of ( sqrt[3]{5 times 25} ) is
A. 5
B. 25
( c cdot 125 )
D. none of these
8
48 Find the smallest number by which 26244 is divided to get the quotient as a perfect cube
A . 4
B. 9
c. 18
D. 36 6
8
49 Evaluate the following:
( (99)^{3} )
8
50 Find the cube root of the number 514
A . 8.0104
B. 8.1104
( c cdot 8.2104 )
D. 8.3104
8
51 State true or false:
100 is a perfect cube
A. True
B. False
8
52 Find the cube root of :
( mathbf{2}^{frac{10}{27}} )
( A cdot 2^{frac{1}{27}} )
B. ( 2^{frac{1}{50}} )
c. ( 2^{frac{5}{5}} )
D. None of these
8
53 ( sqrt[3]{-13824}=? )
A . -24
B. -28
( c .-26 )
D. -34
8
54 Evaluate ( :(98)^{3} ) 8
55 Evaluate :
(i) ( (1.2)^{3} )
(ii) ( (3.5)^{3} )
(iii) ( (0.8)^{3} )
( (i v)(0.5)^{3} )
8
56 Find the smallest number by which 72 must be multiplied, so that the product is a perfect cube
A . 3
B. 6
c. 12
D. 4
8
57 Find the smallest number by which each of the following number must be divided to obtain a perfect cube.
(i) 81
(ii) 128
(iii) 135
(iv) 192
( mathbf{7 0 4} )
(vi) 625
8
58 Solve ( (-10)^{3}+(7)^{3}+(3)^{3} ) 8
59 Find the nearest integer to the cube root
of 46656
8
60 Find the smallest number by which the following number must be divided to obtain a perfect cube 704
A . 1
B. 12
( c cdot 14 )
D. 15
8
61 An odd cube number will have a/an
cube root.
A . odd
B. even
C. fraction
D. none of these
8
62 By what smallest number 29160 be
divided so that the quotient becomes a perfect cube?
8
63 Find the cube root of the following number by prime factorisation method 175616 8
64 What number must be multiplied to ( 6912, ) so that the product becomes a perfect cube?
( A cdot 2 )
B. 3
( c cdot 4 )
D. 6
E . 10
8
65 If ( left(p^{2}+q^{2}right)^{3}=left(p^{3}+q^{3}right)^{2} ) and ( p q neq 0 )
then the value of ( frac{boldsymbol{p}}{boldsymbol{q}}+frac{boldsymbol{q}}{boldsymbol{p}} ) is
8
66 Find the smallest number which should
be multiplied to 392 to make it a
perfect cube.
A . 3
B. 4
( c .5 )
D.
8
67 Find it is a perfect cubes or not?
( mathbf{3 3 7 5} )
8
68 Find the smallest number by which the following number must be divided to obtain a perfect cube:
128
8
69 Cube of all odd natural numbers are odd
A. True
B. False
c. Ambiguous
D. Data insufficient
8
70 Find the smallest number by which 2808 must be multiplied so that the product is a perfect cube. 8
71 The value of ( sqrt[3]{-a^{3}} times sqrt[3]{-b^{3}} ) is
( A cdot a )
B.
( c cdot a b )
D. none of these
8
72 Cube of 1.3 is:
A . 2197
B. 219.7
c. 21.97
D. 2.197
8
73 Which of the following is the cube of odd natural number?
A .32,768
B. 4,096
c. 6,859
D. 1,728
8
74 Find the cube root of the following number by prime factorization method:
( mathbf{1 3 3 1} )
8
75 How many consecutive odd numbers will be needed to obtain the sum of ( 4^{3} ? )
A .2
B. 3
( c cdot 4 )
D.
8
76 Find the smallest no. by which of the following no. must be multiplied to obtain a perfect cube
(i) 243
(ii) 256
(iii) 72
(iv) 675
(v) 100
8
77 The value of ( sqrt[3]{-125 times(-1000)} ) is
A. 50
B. – -50
c. 55
D . -55
8
78 Find the cube root of 3375 by the method of prime factorization.
A . 15
B . 25
c. 35
D. 55
8
79 Find the given number is a perfect cube
or not.
( mathbf{1 3 8 2 4} )
8
80 Find the smallest number that such
must be
subtracted from 220 to make it a
perfect cube
8
81 The number which is not a perfect cube, from the following is:
A. 1,331
B . 216
c. 243
D. 512
8
82 Find the smallest no. by which each of the following no. must be divided to
obtain a perfect cube.
(i) 81
(ii) 128
(iii) 135
(iv) 192
(v) 704
8
83 If the cube root of ( n ) is ( 4, ) then find the
square root of ( n )
A .4
B. 6
( c cdot 8 )
D. 16
8
84 What is the smallest positive integer ( boldsymbol{K} ) such that ( 2000 times 2001 times K ) is a perfect
cube?
A ( cdot 2^{3} times 3^{3} times 23^{3} times 29^{3} )
B . ( 2 times 3 times 23 times 29 )
c. ( 2 times 3^{2} times 23^{3} times 29^{4} )
D . ( 2^{2} times 3^{2} times 23^{2} times 29^{2} )
8
85 Write the units digit of the cube of 833
( A cdot 3 )
B. 7
( c .1 )
D.
8
86 Find the cube root of the number
704969 by looking at the last digit and using estimation
8
87 Find the cube root of the given number through estimation:
( mathbf{2 1 9 7} )
8
88 By what smallest number should we
divide 9000 so that the quotient
becomes a perfect cube. Find the cube
root of the quotient
A . 9,10
B. 9,
( c cdot 19,10 )
D. 19, 5
8
89 Find the product of three consecutive
odd integers, if one of them is ( (2 m+1) )
8
90 Find the cube root of 64 by prime factorisation method. 8
91 Show that ( sqrt[3]{125 times 64}=sqrt[3]{125} times sqrt[3]{64} ) 8
92 What is the cube root of ( -4096 ? )
A . -64
B. -16
c. 16
D. 64
8
93 Cube of all even natural numbers are
even
A . True
B. False
c. Ambiguous
D. Data insufficient
8
94 If ( boldsymbol{x}=mathbf{2}^{mathbf{3}} times mathbf{4}^{mathbf{2}} times mathbf{1} mathbf{7}^{mathbf{3}}, ) then which
number should be divided by ( x ) to get a
perfect cube.
( A cdot 2 )
B. 4
c. 8
D. 17
8
95 Find the two digit number which is a square number and also a cubic
number.
8
96 You are told that 1331 is a perfect cube
Can you guess without factorisation what is its cube root? Similarly, guess the cube root of 4913,12167,32768
8
97 571787 is a perfect cube
Find the cube root of the following number:
8
98 If ( n=67 ) then find the unit digit of
( left[3^{n}+2^{n}right] )
( A )
B. 10
( c cdot 5 )
D. None
8
99 Simplify: ( (-2) times(-3)^{3} ) 8
100 If ( 72 K ) is a perfect cube, then the value
of ( boldsymbol{K} ) is:
( mathbf{A} cdot mathbf{1} )
B . 2
( c .3 )
D.
8
101 Find the given number is a perfect cube
or not.
( mathbf{5 4 0} )
8
102 The cube of an odd natural number is
A. Even
B. Odd
c. May be even, May be odd
D. Prime number
8
103 Find the smallest number by which 33275 must be multiplied so that the product is a perfect cube. 8
104 ( sqrt[3]{-512}=? )
( mathbf{A} cdot-64 )
B . -8
C. Not defined
D. None of these
8
105 Find the cube root of: 175616
A . 56
B. 46
( c .66 )
D. 76
8
106 What is the value of ( sqrt[3]{27} times sqrt[3]{-27} ? )
A . -9
в. -27
c. 9
( D )
8
107 Find the smallest number by which 9000 shoud be divided so that the
quotient becomes a perfect cube?
( A cdot 3 )
B. 9
c. 27
( D )
8
108 Find the smallest number by which
4232 must be multiplied to make it a perfect cube.
A .2
B. 17
c. 19
D. 23
8
109 ( fleft(x+frac{1}{x}right)^{2}=3 ) then find the value of
( boldsymbol{x}^{boldsymbol{6}} )
8
110 By what number 4320 must be multiplied to obtain a number which is a perfect cube?
( mathbf{A} cdot 60 )
B . 45
c. 50
D. 55
8
111 Find the cube root of 27000 by prime factorisation method. 8
112 Multiply 137592 by the smallest number so that the product is a perfect cube. 8
113 Check whether ( 24 x^{3} y^{2} ) is a perfect cube or not. If not, find the smallest number
by which it should be divided to make it a perfect cube. Also, find the cube root of the perfect cube number so obtained.
8
114 The smallest number by which 5400 must be multiplied so that it becomes a perfect cube is:
( mathbf{A} cdot 12 )
B . 10
( c .5 )
D. 3
8
115 Factorise: ( 27 a^{3}+frac{1}{64 b^{3}}+frac{27 a^{2}}{4 b}+frac{9 a}{16 b^{2}} ) 8
116 The smallest natural number by which 36 must be multiplied to get a perfect cube is
( A cdot 6 )
в. 216
( c cdot 45 )
D.
8
117 Find the smallest number which when
multiplied with 53240 will make the product a perfect cube.
8
118 The sum of the cubes of three
consecutive natural numbers is
divisible by
A. 7
B. 9
( c cdot 25 )
D. 26
8
119 ( (a+b)^{3}=? )
( mathbf{A} cdot a^{3}+3 a^{2} b+3 a b^{2}+b^{3} )
B ( cdot a^{3}+a^{2} b+a b^{2}+b^{3} )
c. ( a^{3}-3 a^{2} b+3 a b^{2}-b^{3} )
D ( cdot a^{3}+3 a^{2} b-3 a b^{2}+b^{3} )
8
120 Fill in the blanks:
( sqrt[3]{ldots ldots . .}=sqrt[3]{boldsymbol{4}} times sqrt[3]{mathbf{5}} times sqrt[3]{boldsymbol{6}} )
8
121 How will you represent 49 in cube root?
A ( cdot sqrt[7]{49} )
B. ( sqrt[2]{49} )
( c cdot sqrt[4]{49} )
D. ( sqrt[3]{49} )
8
122 If the square root of a number is
between 6 and ( 7, ) then its cube root lies between
( mathbf{A} cdot 2,3 )
в. 2.5,3
( c .3,4 )
D. 4,4.5
8
123 392 is a perfect cube
A. True
B. False
c. Ambiguous
D. Insufficient information
8
124 Find the cube root of a given number by prime factorization method.
27000
8
125 What is a smallest number by which 2560 is to be multiplied so that the product is a perfect cube? 8
126 On multiplying 137592 by the smallest number ( _{–}-_{-}- ) the product is a perfect cube, the cube root of this perfect cube number is
A ( cdot 7 times 13^{2}, 546 )
В. ( 7 times 13^{3}, 546 )
c. ( 5 times 13,546 )
D. ( 7 times 13^{4}, 546 )
8
127 If ( boldsymbol{a}+boldsymbol{b}+boldsymbol{c}=mathbf{0}, ) then ( boldsymbol{a}^{3}+boldsymbol{b}^{3}+boldsymbol{c}^{3}= )
( k a b c, ) the value of ( ^{prime} k^{prime} ) is
8
128 Find the cube root of 512 8
129 Find the cube root of :
( mathbf{1} )
( mathbf{A} cdot mathbf{1} )
B. 2
c. Does not exist
D. None of these
8
130 Find the cube root of 0.000000027
A . 0.03
B. 0.3
c. 0.003
D. 0.0003
8
131 Is 243 a perfect cube? If not find the
smallest number by which 243 must be multiplied to get a perfect cube
8
132 From the following options, choose the option with which perfect answer does not ends with
A . 5
B. 4
( c cdot 0 )
D. None of the above
8
133 The value of ( sqrt[3]{-512} times sqrt[3]{8} ) is ( ldots )
A . -16
B. 4
( c cdot-5 )
( D cdot-4 )
8
134 By what smallest number should we
multiply 8788 so that the product becomes a perfect cube. Find the cube
root of the product
A .2,26
B. 2,6
c. 22,26
D. 22, 21
8
135 Evaluate: ( sqrt[3]{frac{216}{2197}} )
( A cdot frac{6}{13} )
в. ( frac{7}{13} )
( c cdot frac{8}{13} )
D. ( frac{4}{13} )
8
136 What is the smallest number by which 1600 is to be divided, so that the quotient is a perfect cube? 8
137 What is the least number by which 8640 is divided, the quotient as a
complete cube number?
( A cdot 6 )
B. 7
( c cdot 5 )
D. 8
8
138 The value of ( (3.1)^{3} ) is
A . 27.971
B. 29.791
c. 29.97
D. 27.197
8
139 Evaluate the cube root of: ( sqrt[3]{343} ) 8
140 Find the smallest number by which the number 108 must be multiplied to obtain a perfect cube
A .2
B. 3
( c cdot 4 )
D. 5
8
141 What will be the unit digit of ( (87)^{75^{63}} ) 8
142 Check whether the following are perfect cubes?
(i) 400
(ii) 216
(iii) 729
(iv) 250
(v) 1000
(vi) 900
8
143 Which of the following number has same unit digit as its cube?
( begin{array}{l}text { A } cdot 122^{3} \ ^{3}end{array}^{1}^{32} )
B. ( 168^{3} )
( mathbf{c} cdot 137^{3} )
D. ( 184^{3} )
8
144 Which one of the following numbers is not a complete cube? 64,216,343,256
A . 64
в. 216
c. 343
D. 256
8
145 Find the cubes of the following
numbers:
( mathbf{3 0 2} )
8
146 which of the following numbers are the cubes of following numbers:
(i) 216
(ii) 729
(iii) 512
( (i v) 3375 )
(v) 1000
8
147 Evaluate using identities ( 6^{3}-9^{3}+3^{3} )
( mathbf{A} cdot-486 )
в. 486
( c .-86 )
D. None of these
8
148 Find the unit digit of the cube root of the following number:
( mathbf{1 7 5 6 1 6} )
A . 5
B. 6
c. 8
D. 9
8
149 State True or False
Cube of any odd number is even
A. True
B. False
c. Ambiguous
D. Data insufficient
8
150 Write cubes of 5 natural numbers which
are of the form ( 3 n+1(e . g .4,7,10,, . . .) ) and
verify the following:
‘The cube of a natural number of the
form ( 3 n+1 ) is a natural number of the
same form’.
8
151 Write the units digit of the cube for
( mathbf{5 9 2 2} )
A . 8
B. 4
( c .6 )
D. none of these
8
152 Find the value of ( left(1^{3}+2^{3}+3^{3}right)^{frac{1}{2}} ) 8
153 Find the smallest number by which the following number must be multiplied to obtain a perfect cube 243
( A cdot 3 )
B.
( c cdot 0 )
D.
8
154 Find the cube of 30 8
155 Cube of any positive integer is of the form ( 9 m, 9 m+1 ) or ( 9 m+8, ) where ( m ) is
a non-negative integer.
A. True
B. False
c. Neither
D. Either
8
156 ( frac{4}{9^{frac{1}{3}}-3^{frac{1}{3}}+1} ) is equal to
( A cdot 3^{frac{1}{5}}+1 )
B. ( 3^{frac{1}{5}}-1 )
c. ( 3^{frac{1}{5}}+2 )
D. ( 3^{frac{1}{5}}-2 )
8
157 By which smallest number must the
following numbers be divided so that the quotient is a perfect cube?
( mathbf{7 8 0 3} )
8
158 By what least number 4320 be multiplied to become a perfect cube?
A . 10
B. 30
c. 20
D. 50
8
159 What smallest number should 7803 be
multiplied with so that the product becomes a perfect cube
8
160 Is there any number whose perfect cube
ends with ( 8 ? )
(Yes or No)
8
161 If ( a^{2} ) ends in ( 9, ) then ( a^{3} ) will end in:
( A cdot 7 )
B. 3
c. 5
D. none of the above
8
162 Find the cube root of the following numbers by prime fractorisaiton method.
( mathbf{3 4 3} )
( mathbf{4 0 9 6} )
( mathbf{5 8 3 2} )
( mathbf{1 2 5 0 0 0} )
8
163 How many consecutive odd numbers are needed to make sum as ( 13^{3} ? )
A. 11
B . 13
( c .15 )
D. 17
8
164 Find the smallest number by which 128
must be divided so that the result is a
perfect cube.
8
165 State true or false
If square of a number ends with ( 5, ) then
its cube ends with 25
A. True
B. False
c. Ambiguous
D. Data insufficient
8
166 The sum of any number of consecutive cubes beginning with 1 is always a:
A. perfect square
B. perfect cube
c. odd number
D. even number
8
167 Which of the following numbers are not perfect cubes?
(i) 128
(ii) 100
(iii) 64
(iv) 125
( mathbf{7 2} quad(mathbf{v i}) mathbf{6 2 5} )
8
168 Find the cube root of each of the
following numbers by prime factorisation method
512
( A cdot 6 )
B. 8
( c cdot 7 )
D.
8
169 ( boldsymbol{x}^{boldsymbol{3}}+boldsymbol{x}^{boldsymbol{3}}+boldsymbol{x}=? )
if ( boldsymbol{x}=boldsymbol{7} )
8
170 8640 is not a perfect cube
A. True
B. False
c. Ambiguous
D. Insufficient information
8
171 Find the value of the following:
(i) ( 15^{3} ) (ii) ( (-4)^{3} )
(iii) ( (1.2)^{3}(text { iv })left(frac{-3}{4}right)^{3} )
8
172 The cube root of a number is a number
when ( _{text {一一一一一一 }} ) three times gives that
number.
A. divided
B. addedd
c. subtracted
D. multiplied
8
173 If ( sqrt[3]{mathbf{7 2} times boldsymbol{A}}=mathbf{1 2}, ) then find the value of
( boldsymbol{A} )
A . 12
B . 24
( c .36 )
D. 6
8
174 If ( a+b+c=0 ) then prove that ( a^{3}+ )
( b^{3}+c^{3}=3 a b c )
8
175 Show that 6 is not a perfect cube 8
176 The value of ( sqrt{1^{3}+2^{3}+3^{3}} ) is
A. 5
B. 6
( c cdot 7 )
D. 8
8
177 ( sqrt[3]{27000}= )
A . 300
в. 3000
( c .30 )
D. 900
8
178 ( ln (46)^{13} ) unit digit is 6 8
179 Find the cube root of 15625 by prime factorization method. 8
180 The cube of an odd natural number is
always
A. Even
B. Odd
c. Even or odd
D. Can’t say
8
181 Find the cube of 133: 8
182 The value of ( sqrt[3]{5 times 25} ) is
A. 5
B. 25
( c cdot 1 )
D. 125
8
183 What is the smallest number by which
18522 must be divided so that the
quotient is a perfect cube?
8
184 The cube of two digit number may have seven or more digits
A. True
B. False
c. Ambiguous
D. Data insufficient
8
185 What is the smallest positive number
greater than 1 which is a cube as well
as a square?
A . 8
B. 64
( c cdot 72 )
D. 144
8
186 The smallest number by which 3600 can be divided to make it a perfect cube is:
( A cdot 9 )
B. 50
( c .300 )
D. 450
8
187 Find the smallest number which should
be multiplied to 10584 to get a perfect
cube.
8
188 Find the smallest number by which 128
must be divided, so that the quotient is a perfect cube
A .2
B. 3
( c cdot 7 )
D. 12
8
189 A number ( a ) is called a perfect cube if
there exists a natural number ( b ) such
that
A. ( a=b times b times b )
( b )
В. ( b=a times a times a )
( c, a=a times b times a )
( a )
D. ( a=a times b times b )
8
190 Cube of odd natural number is
number
A . odd
B. even
c. negative
D. prime
8
191 Find the smallest number by which 64
must be divided so that the result is a
perfect cube.
8
192 Write the units digit of the cube for 7171
( A cdot 1 )
B. 2
( c .5 )
D. 3
8
193 13. (1) 343-7
(3) 2166
2 5168
4729-9
8
194 Divide the number 26244 by the
smallest number so that the quotient is a perfect cube
8
195 Find the cube root of each of the
following cube numbers through
estimation.
( mathbf{8 5 1 8 4} )
8
196 Find the smallest number by which 8788 must be multiplied to obtain a perfect cube. 8
197 If ( 72 K ) is a perfect cube, find the value
of ( boldsymbol{K} )
( mathbf{A} cdot mathbf{1} )
B . 2
( c .3 )
D.
8
198 What will be the unit digit of ( 137959^{3} )
( mathbf{A} cdot mathbf{1} )
B. 3
( c .6 )
D.
8
199 If the unit place of a number is ( 7, ) then find the unit digit of its cube.
A . 1
B. 3
c. 5
( D )
8
200 In the five digit number ( 1 b 6 a 3, ) a is the
greatest single digit perfect cube and twice of it exceeds by ( 7 . ) Then the sum of the number and its cube root is
( mathbf{A} cdot 18700 )
B. 11862
c. 19710
D. 25320
8
201 Find the smallest number which should
be multiplied to 15625 to get a perfect
cube.
8
202 By what smallest number 5184 be
divided, so what the resulting number becomes a perfect cube?
8
203 Find the smallest number which should
be multiplied to 1352 to get a perfect
cube.
( mathbf{A} cdot 12 )
B . 13
c. 61
D. 21
8
204 Factorise ( 8 x^{3}+27 y^{3}+36 x^{3} y+54 x y^{2} ) 8
205 Evaluate ( : 125 sqrt[3]{a^{6}}-sqrt[3]{125 a^{6}} ) 8
206 Find the cube root of 125 8
207 What is the smallest number by which
1600 must be divided so that the
quotient is a perfect cube?
8
208 Value of ( sqrt[3]{343} ) is:
A. 7
B. – 5
( c cdot frac{7}{5} )
D.
8
209 Find the cube root of 5832 8
210 To cube a number, how many times you need to multiply the number with itself?
A. 1 time
B. 2 times
c. 3 times
D. 4 times
8
211 What is the value of ( sqrt[3]{-8}-sqrt[3]{-216} ? )
A . -8
B. -4
( c cdot 4 )
D.
8
212 Find the smallest number that must be
subtracted from 6868 to make it a
perfect cube.
8
213 Simplify: ( sqrt[3]{frac{216}{2197}} )
( A cdot frac{36}{27} )
в. ( frac{66}{23} )
( c cdot frac{6}{13} )
D. None of the above
8
214 Which of the following statements is
true?
A. Cube root of a positive number may be a negative number
B. Cube root of a number ending with 8 ends with 2 .
C. Cube root of an odd number may be an even number.
D. All above statements are false
8
215 ( sqrt{sqrt[3]{125+sqrt{24}}} ) is equal to
( A cdot sqrt{5}-1 )
B. ( sqrt{3}+sqrt{2} )
c. ( sqrt{3}+1 )
D. ( sqrt{5}+sqrt{2} )
8
216 Find the smallest number by which 243 must be multiplied to make it a perfect
cube.
A . 1
B. 2
( c .3 )
D. 4
8
217 Which of the following numbers are not perfect cubes?
1. २१६
2. 125
3.1000
4.46656
8
218 The smallest natural number by which 1296 be divided to get a perfect cube is
A . 16
B. 6
( c cdot 60 )
D. none of these
8
219 Write the value of ( 25^{3}-75^{3}+50^{3} ) 8
220 Is the following number a perfect cube?
( mathbf{4 6 6 5 6} )
Say yes or no.
A. Yes
B. No
c. Ambiguous
D. Data insufficient
8
221 The sum of any three distinct natural
numbers arranged in ascending order is 200 such that the second number is a
perfect cube. How many possible values are there for this number?
( A cdot 4 )
B. 3
c. 2
( D )
8
222 ( ln (25)^{15} ) unit digit is 5 8
223 State true or false:
If a number ends with ( 5, ) then its cube
ends with 5
A. True
B. False
8
224 Solved:
( sqrt[3]{64} )
8
225 Find the cube root of 512 by prime factorisation method: 8
226 Find the cube root of each of the
following numbers by prime Factorization method:
(i) 729
(ii) 343
(iii) ( 512(text { iv ) } 0.064 )
( mathbf{0 . 2 1 6} )
( (v i) 5 frac{23}{64}(v i i)-1.331(v i i i) )
-27000
8
227 Write an equivalent exponential form for radical expression. ( sqrt[3]{13} ) 8
228 If the cube root of a number, which is 8
more than a number ( n ) equals ( -0.5, ) find
the value of ( n )
A . -15.625
в. -8.794
c. -8.125
D. -7.875
E . 421.875
8
229 Find the cube root of the following number by prime factorization method:
2744
8
230 Find the cube root of the following number by prime factorization method:
( mathbf{2 7 0 0 0} )
( A .30 )
B . 40
c. 50
D. 80
8
231 Find the negative of cube root of
-2744000:
8
232 What will be the unit digit of ( 98765^{3} )
( mathbf{A} cdot mathbf{5} )
B. 0
( c cdot 2 )
D. 3
8
233 Find the smallest number by which each of the following number must be multiplied to obtain a perfect cube.
(i) 243
(ii) 256
(iii) 72
(iv) 675
( mathbf{1 0 0} )
8
234 Looking at the pattern, fill in the gaps in the following
( mathbf{3} )
( 4 quad-5 )
, and
( begin{array}{cccc}2^{3}= & 3^{3}= & ldots= & ldots ldots \ 8 & ldots ldots & 64 & ldotsend{array} )
8
235 If we wrote ( n^{3} ) as the sum of
consecutive odd numbers then what
will be the first term.
( mathbf{A} cdot 2 n+1 )
B. ( (2 n+1)(2 n-1) )
c. ( 2 n-1 )
D. ( n(n-1)+1 )
8

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