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 NoQuestionsClass
1Examine 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
2127
343 is equal to
13
(3) 9
(2) 1-2
(41-2
8
3The cube root of 4.096 is
A . 1.6
B. 1.7
( c cdot 1.8 )
D. 2.6
8
4Find the cube root of 614125 using
prime factorization:
A . 65
B. 75
c. 85
D. 95
8
5Find 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
6Estimate the value of cube root of the
number 1333
A . 10.99
B. 20.10
c. 12.45
D. 10.56
8
7Represent the number 19 as the
difference between the cubes of natural
numbers.
8
8If ( 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
9The cube of a two digit number may be a three digit number.
A. True
B. False
c. Insufficient Data
D. None of these
8
10Find the digit at unit’s place of ( 128^{3} )
( A cdot 8 )
B. 6
( c cdot 4 )
D. 2
8
11Find the cubes of the following
numbers:
40
8
12A perfect cube does not end with two
zeros
A. True
B. False
c. Ambiguous
D. Data insufficient
8
13Cubes of Negative integers are negative
A. True
B. False
c. Ambiguous
D. Data insufficient
8
14Find the cube root of
( 99-70 sqrt{2} )
8
15Find the smallest number that must be
added to 400 to make it a perfect cube
A . 108
в. 112
c. 18
D. 12
8
16The cube of a two digit number may have seven or more digits.
A. True
B. False
c. Insufficient Data
D. None of these
8
17If 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
18If ( 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
19Write the units digit of the cube for 109
( A cdot 1 )
B. 7
( c .9 )
D. 3
8
20The value of ( (27 times 2744)^{frac{1}{3}} ) is
A . 40
B. 42
c. 22
D. 32
8
21Find the smallest number by which a
given number must be multiplied to obtain a perfect cube 72
8
22Find the value of ( (47)^{3} ) using the shortcut or column method8
23Find the smallest number by which a given number must be divided to obtain
a perfect cube 704
8
24Find the nearest integer to the cube root
of 331776:
8
25Evaluate the following:
( mathbf{1 0 4}^{mathbf{3}}+mathbf{9 6}^{mathbf{3}} )
8
26Find the cube root of 39304 by estimation method.
A . 24
B. 44
( c .34 )
D. 54
8
27Evaluate the following:
( 46^{3}+34^{3} )
8
2864. 553 + 173 – 723 + 201960 is
equal to
(1)-1
(2) O
(3) 1
(4) 17
8
29Find the smallest number by which a given number must be divided to obtain
a perfect cube
81
8
30What 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
31Cube of 1.5 is:
( mathbf{A} cdot 3.375 )
B. 33.75
c. 3.125
D. 31.25
8
32How many consecutive odd numbers are required to form ( 10^{3} ) as their sum?
A . 10
B. 11
( c .9 )
D. 20
8
33The 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
34Find 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
35The prime factor of 128 is
A. 0
B. 1
( c cdot 2 )
D. 3
8
36( ln (34)^{33} ) unit digit is 48
37If ( 27=a^{3}, ) find the value of ( a )
( mathbf{A} cdot mathbf{1} )
B . 2
( c .3 )
D. 4
8
38If cube of ( 1 frac{2}{3}, ) is of the form ( frac{a}{b}, ) then ( a+ )
( b ) is equal to:
8
39Find the cube root of each of the
following numbers by prime factorisation method:
13824
A . 14
B . 24
( c .34 )
D. 44
8
40What 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
41The 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
42Find the cube root of :
8
8
43Find the smallest number which should
be multiplied to 100 to get a perfect
cube.
8
44Which 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
45The cube root of any multiple of 8 is always divisible by:
A . 2
B. 4
c. 8
D. 16
8
46Cube of any odd number is even
A. True
B. False
c. Depends on the number
D. Data Insufficient
8
47The value of ( sqrt[3]{5 times 25} ) is
A. 5
B. 25
( c cdot 125 )
D. none of these
8
48Find 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
49Evaluate the following:
( (99)^{3} )
8
50Find the cube root of the number 514
A . 8.0104
B. 8.1104
( c cdot 8.2104 )
D. 8.3104
8
51State true or false:
100 is a perfect cube
A. True
B. False
8
52Find 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
54Evaluate ( :(98)^{3} )8
55Evaluate :
(i) ( (1.2)^{3} )
(ii) ( (3.5)^{3} )
(iii) ( (0.8)^{3} )
( (i v)(0.5)^{3} )
8
56Find 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
57Find 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
58Solve ( (-10)^{3}+(7)^{3}+(3)^{3} )8
59Find the nearest integer to the cube root
of 46656
8
60Find 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
61An odd cube number will have a/an
cube root.
A . odd
B. even
C. fraction
D. none of these
8
62By what smallest number 29160 be
divided so that the quotient becomes a perfect cube?
8
63Find the cube root of the following number by prime factorisation method 1756168
64What 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
65If ( 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
66Find the smallest number which should
be multiplied to 392 to make it a
perfect cube.
A . 3
B. 4
( c .5 )
D.
8
67Find it is a perfect cubes or not?
( mathbf{3 3 7 5} )
8
68Find the smallest number by which the following number must be divided to obtain a perfect cube:
128
8
69Cube of all odd natural numbers are odd
A. True
B. False
c. Ambiguous
D. Data insufficient
8
70Find the smallest number by which 2808 must be multiplied so that the product is a perfect cube.8
71The 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
72Cube of 1.3 is:
A . 2197
B. 219.7
c. 21.97
D. 2.197
8
73Which of the following is the cube of odd natural number?
A .32,768
B. 4,096
c. 6,859
D. 1,728
8
74Find the cube root of the following number by prime factorization method:
( mathbf{1 3 3 1} )
8
75How many consecutive odd numbers will be needed to obtain the sum of ( 4^{3} ? )
A .2
B. 3
( c cdot 4 )
D.
8
76Find 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
77The value of ( sqrt[3]{-125 times(-1000)} ) is
A. 50
B. – -50
c. 55
D . -55
8
78Find the cube root of 3375 by the method of prime factorization.
A . 15
B . 25
c. 35
D. 55
8
79Find the given number is a perfect cube
or not.
( mathbf{1 3 8 2 4} )
8
80Find the smallest number that such
must be
subtracted from 220 to make it a
perfect cube
8
81The number which is not a perfect cube, from the following is:
A. 1,331
B . 216
c. 243
D. 512
8
82Find 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
83If the cube root of ( n ) is ( 4, ) then find the
square root of ( n )
A .4
B. 6
( c cdot 8 )
D. 16
8
84What 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
85Write the units digit of the cube of 833
( A cdot 3 )
B. 7
( c .1 )
D.
8
86Find the cube root of the number
704969 by looking at the last digit and using estimation
8
87Find the cube root of the given number through estimation:
( mathbf{2 1 9 7} )
8
88By 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
89Find the product of three consecutive
odd integers, if one of them is ( (2 m+1) )
8
90Find the cube root of 64 by prime factorisation method.8
91Show that ( sqrt[3]{125 times 64}=sqrt[3]{125} times sqrt[3]{64} )8
92What is the cube root of ( -4096 ? )
A . -64
B. -16
c. 16
D. 64
8
93Cube of all even natural numbers are
even
A . True
B. False
c. Ambiguous
D. Data insufficient
8
94If ( 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
95Find the two digit number which is a square number and also a cubic
number.
8
96You 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
97571787 is a perfect cube
Find the cube root of the following number:
8
98If ( n=67 ) then find the unit digit of
( left[3^{n}+2^{n}right] )
( A )
B. 10
( c cdot 5 )
D. None
8
99Simplify: ( (-2) times(-3)^{3} )8
100If ( 72 K ) is a perfect cube, then the value
of ( boldsymbol{K} ) is:
( mathbf{A} cdot mathbf{1} )
B . 2
( c .3 )
D.
8
101Find the given number is a perfect cube
or not.
( mathbf{5 4 0} )
8
102The cube of an odd natural number is
A. Even
B. Odd
c. May be even, May be odd
D. Prime number
8
103Find 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
105Find the cube root of: 175616
A . 56
B. 46
( c .66 )
D. 76
8
106What is the value of ( sqrt[3]{27} times sqrt[3]{-27} ? )
A . -9
в. -27
c. 9
( D )
8
107Find 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
108Find 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
110By 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
111Find the cube root of 27000 by prime factorisation method.8
112Multiply 137592 by the smallest number so that the product is a perfect cube.8
113Check 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
114The 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
115Factorise: ( 27 a^{3}+frac{1}{64 b^{3}}+frac{27 a^{2}}{4 b}+frac{9 a}{16 b^{2}} )8
116The 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
117Find the smallest number which when
multiplied with 53240 will make the product a perfect cube.
8
118The 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
120Fill in the blanks:
( sqrt[3]{ldots ldots . .}=sqrt[3]{boldsymbol{4}} times sqrt[3]{mathbf{5}} times sqrt[3]{boldsymbol{6}} )
8
121How 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
122If 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
123392 is a perfect cube
A. True
B. False
c. Ambiguous
D. Insufficient information
8
124Find the cube root of a given number by prime factorization method.
27000
8
125What is a smallest number by which 2560 is to be multiplied so that the product is a perfect cube?8
126On 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
127If ( 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
128Find the cube root of 5128
129Find the cube root of :
( mathbf{1} )
( mathbf{A} cdot mathbf{1} )
B. 2
c. Does not exist
D. None of these
8
130Find the cube root of 0.000000027
A . 0.03
B. 0.3
c. 0.003
D. 0.0003
8
131Is 243 a perfect cube? If not find the
smallest number by which 243 must be multiplied to get a perfect cube
8
132From 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
133The value of ( sqrt[3]{-512} times sqrt[3]{8} ) is ( ldots )
A . -16
B. 4
( c cdot-5 )
( D cdot-4 )
8
134By 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
135Evaluate: ( sqrt[3]{frac{216}{2197}} )
( A cdot frac{6}{13} )
в. ( frac{7}{13} )
( c cdot frac{8}{13} )
D. ( frac{4}{13} )
8
136What is the smallest number by which 1600 is to be divided, so that the quotient is a perfect cube?8
137What 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
138The value of ( (3.1)^{3} ) is
A . 27.971
B. 29.791
c. 29.97
D. 27.197
8
139Evaluate the cube root of: ( sqrt[3]{343} )8
140Find 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
141What will be the unit digit of ( (87)^{75^{63}} )8
142Check whether the following are perfect cubes?
(i) 400
(ii) 216
(iii) 729
(iv) 250
(v) 1000
(vi) 900
8
143Which 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
144Which one of the following numbers is not a complete cube? 64,216,343,256
A . 64
в. 216
c. 343
D. 256
8
145Find the cubes of the following
numbers:
( mathbf{3 0 2} )
8
146which of the following numbers are the cubes of following numbers:
(i) 216
(ii) 729
(iii) 512
( (i v) 3375 )
(v) 1000
8
147Evaluate using identities ( 6^{3}-9^{3}+3^{3} )
( mathbf{A} cdot-486 )
в. 486
( c .-86 )
D. None of these
8
148Find 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
149State True or False
Cube of any odd number is even
A. True
B. False
c. Ambiguous
D. Data insufficient
8
150Write 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
151Write the units digit of the cube for
( mathbf{5 9 2 2} )
A . 8
B. 4
( c .6 )
D. none of these
8
152Find the value of ( left(1^{3}+2^{3}+3^{3}right)^{frac{1}{2}} )8
153Find 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
154Find the cube of 308
155Cube 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
157By which smallest number must the
following numbers be divided so that the quotient is a perfect cube?
( mathbf{7 8 0 3} )
8
158By what least number 4320 be multiplied to become a perfect cube?
A . 10
B. 30
c. 20
D. 50
8
159What smallest number should 7803 be
multiplied with so that the product becomes a perfect cube
8
160Is there any number whose perfect cube
ends with ( 8 ? )
(Yes or No)
8
161If ( a^{2} ) ends in ( 9, ) then ( a^{3} ) will end in:
( A cdot 7 )
B. 3
c. 5
D. none of the above
8
162Find 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
163How many consecutive odd numbers are needed to make sum as ( 13^{3} ? )
A. 11
B . 13
( c .15 )
D. 17
8
164Find the smallest number by which 128
must be divided so that the result is a
perfect cube.
8
165State 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
166The 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
167Which 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
168Find 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
1708640 is not a perfect cube
A. True
B. False
c. Ambiguous
D. Insufficient information
8
171Find the value of the following:
(i) ( 15^{3} ) (ii) ( (-4)^{3} )
(iii) ( (1.2)^{3}(text { iv })left(frac{-3}{4}right)^{3} )
8
172The 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
173If ( 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
174If ( a+b+c=0 ) then prove that ( a^{3}+ )
( b^{3}+c^{3}=3 a b c )
8
175Show that 6 is not a perfect cube8
176The 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 68
179Find the cube root of 15625 by prime factorization method.8
180The cube of an odd natural number is
always
A. Even
B. Odd
c. Even or odd
D. Can’t say
8
181Find the cube of 133:8
182The value of ( sqrt[3]{5 times 25} ) is
A. 5
B. 25
( c cdot 1 )
D. 125
8
183What is the smallest number by which
18522 must be divided so that the
quotient is a perfect cube?
8
184The cube of two digit number may have seven or more digits
A. True
B. False
c. Ambiguous
D. Data insufficient
8
185What 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
186The 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
187Find the smallest number which should
be multiplied to 10584 to get a perfect
cube.
8
188Find 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
189A 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
190Cube of odd natural number is
number
A . odd
B. even
c. negative
D. prime
8
191Find the smallest number by which 64
must be divided so that the result is a
perfect cube.
8
192Write the units digit of the cube for 7171
( A cdot 1 )
B. 2
( c .5 )
D. 3
8
19313. (1) 343-7
(3) 2166
2 5168
4729-9
8
194Divide the number 26244 by the
smallest number so that the quotient is a perfect cube
8
195Find the cube root of each of the
following cube numbers through
estimation.
( mathbf{8 5 1 8 4} )
8
196Find the smallest number by which 8788 must be multiplied to obtain a perfect cube.8
197If ( 72 K ) is a perfect cube, find the value
of ( boldsymbol{K} )
( mathbf{A} cdot mathbf{1} )
B . 2
( c .3 )
D.
8
198What will be the unit digit of ( 137959^{3} )
( mathbf{A} cdot mathbf{1} )
B. 3
( c .6 )
D.
8
199If the unit place of a number is ( 7, ) then find the unit digit of its cube.
A . 1
B. 3
c. 5
( D )
8
200In 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
201Find the smallest number which should
be multiplied to 15625 to get a perfect
cube.
8
202By what smallest number 5184 be
divided, so what the resulting number becomes a perfect cube?
8
203Find 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
204Factorise ( 8 x^{3}+27 y^{3}+36 x^{3} y+54 x y^{2} )8
205Evaluate ( : 125 sqrt[3]{a^{6}}-sqrt[3]{125 a^{6}} )8
206Find the cube root of 1258
207What is the smallest number by which
1600 must be divided so that the
quotient is a perfect cube?
8
208Value of ( sqrt[3]{343} ) is:
A. 7
B. – 5
( c cdot frac{7}{5} )
D.
8
209Find the cube root of 58328
210To 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
211What is the value of ( sqrt[3]{-8}-sqrt[3]{-216} ? )
A . -8
B. -4
( c cdot 4 )
D.
8
212Find the smallest number that must be
subtracted from 6868 to make it a
perfect cube.
8
213Simplify: ( 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
214Which 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
216Find the smallest number by which 243 must be multiplied to make it a perfect
cube.
A . 1
B. 2
( c .3 )
D. 4
8
217Which of the following numbers are not perfect cubes?
1. २१६
2. 125
3.1000
4.46656
8
218The 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
219Write the value of ( 25^{3}-75^{3}+50^{3} )8
220Is 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
221The 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 58
223State true or false:
If a number ends with ( 5, ) then its cube
ends with 5
A. True
B. False
8
224Solved:
( sqrt[3]{64} )
8
225Find the cube root of 512 by prime factorisation method:8
226Find 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
227Write an equivalent exponential form for radical expression. ( sqrt[3]{13} )8
228If 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
229Find the cube root of the following number by prime factorization method:
2744
8
230Find 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
231Find the negative of cube root of
-2744000:
8
232What will be the unit digit of ( 98765^{3} )
( mathbf{A} cdot mathbf{5} )
B. 0
( c cdot 2 )
D. 3
8
233Find 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
234Looking 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
235If 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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