Squares And Square Roots Questions

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

List of squares and square roots Questions

Question No Questions Class
1 Write the following in the expanded
form:
( (m+2 n-5 p)^{2} )
8
2 Find the smallest number by which 12748 be multiplied so that the product is a perfect square.
A. 3187
в. 7814
c. 4577
D. 1842
8
3 14. Evaluate: 11.96. 8
4 If ( x^{2}+frac{1}{x^{2}}=18, ) then the value of
( left(x+frac{1}{x}right) ) is ( ? )
A .
B. 3
c. ( sqrt{20} )
D. 6
8
5 For each of the following, find the least number that must be added so that the
resulting number is a perfect square. 55078
A . 157
B. 147
( c cdot ) 156
D. 164
8
6 Find the smallest whole number by
which 252 should be divided, so as to
get a perfect square.
8
7 4.
The square of an odd number is always odd.
V
*
*
mir
ou Foque PP a
8
8 12.
Which one of the following num-
bers lacks the common property
in the series?
81, 36, 25, 9, 5, 16
(1) 5
(2) 9
(3) 36
(4) 25
8
9 5.
If’a’ is a square root of ‘b’ then ‘b’is ………….. of‘a’.
6
A number whose sauare root is avant in animda
8
10 If ( a=0.1039 ), then the value of
( sqrt{4 a^{2}-4 a+1}+3 a ) is:
A . 0.1039
B. 0.2078
c. 1.1039
D . 2.1039
8
11 ( left[left(frac{x^{2}}{sqrt{1+x^{2}}}+frac{1}{sqrt{1+x^{2}}}right)^{2}right] ) 8
12 Find the square root of the following numbers by the factorisation numbers:
82944
8
13 Use identities to evaluate ( (mathbf{9 7})^{2} )
A. 9,109
B. 9,409
c. 9,909
D. 9,209
8
14 Find the following squares by using the identity
( left(frac{x^{2}}{y z}+frac{y^{2}}{x z}right)^{2} )
8
15 Use division method of contradiction to
show that ( sqrt{3} ) and ( sqrt{5} ) are irrational numbers. Also find the value of ( sqrt{15} times ) ( sqrt{3} times sqrt{5} )
8
16 10. If (2 x 9) (2 x 9) is 324, then find the value of
324.
8
17 65. Find the simplest value
of 250 + V18 – 72 (given 2
= 1.414).
(1) 4.242 (2) 9.898
(3) 10.312 (4) 8.484
8
18 By splitting into prime factors, find the square root of 729
A . 27
B. 21
c. 17
D. 87
8
19 By using identity.
( (mathbf{7} 99)^{2}=? )
8
20 What is ten times the square root of the
following decimal number:
( mathbf{7 . 2 9} )
8
21 Find the square root of the following number by Division method.
( mathbf{1 3 6 9} )
8
22 6.
How many natural numbers lie between squares of 12
and 13.
8
23 Simplify:
( (boldsymbol{a}+boldsymbol{b}+boldsymbol{c})^{2}+(boldsymbol{a}-boldsymbol{b}+boldsymbol{c})^{2}+ )
( (a+b-c)^{2} )
8
24 Evaluate the following by using the
identities:
( 48^{2} )
8
25 The least number by which 216 must be divided to make the result a
perfect square, is
( A cdot 3 )
B. 4
( c cdot 6 )
D.
8
26 Evaluate ( left(17^{2}-8^{2}right)^{frac{1}{2}} ) 8
27 Evaluate: ( sqrt{mathbf{1 0 0}}+sqrt{mathbf{4 9}} )
A. ( sqrt{149} )
B. ( sqrt{490} )
c. ( sqrt{10}+sqrt{14} )
D. 17
8
28 Find the least number which must be
added to the following number so as to get a perfect square:
6412
A .52
в. 149
( c .63 )
D. 112
8
29 DU, SMISLU 014 “uglis w is a pellet syuare 15
– IVET
9. 7396 students are sitting in an auditorium in such a manner that there are as many students in a row as there are rows in the
auditorium. How many rows are there in the auditorium?
Sol. Let number of students sitting in a row=’x’
8
30 Find the squares of 510 using the identity
( (a+b)^{2}=a^{2}+2 a b+b^{2} )
8
31 Find the square root of 13.31 using long
division method.
8
32 Express 49 as the sum of 7 odd natural numbers.
1
1:.
1.
.
8
33 Square numbers can only have………….. number of zeros a
the end.
The number of merced at the end of the square of a numbe
8
34 Find the square root of 8100 by the
prime factorisation method.
( A cdot 80 )
B. 90
( c .30 )
D. 70
8
35 ( sqrt{(12+sqrt{12+sqrt{12+ldots}})}=x, ) then
the value of ( x ) is
( A cdot 3 )
B. 4
( c cdot 6 )
D. Greater than 6
8
36 Evaluate ( left(frac{2 x}{7}-frac{7 y}{4}right)^{2} )
A ( cdot frac{x^{2}}{49}+frac{17 y^{2}}{16}-x y )
B. ( frac{4 x^{2}}{49}+frac{49 y^{2}}{16}-x y )
C ( cdot frac{4 x^{2}}{9}+frac{49 y^{2}}{4}-x y )
D. ( frac{x^{2}}{13}+frac{49 y^{2}}{13}-x y )
8
37 Find the least number which must be
added to the following number so as to get a perfect square. 1750
A . 26
в. 209
c. 14
D. 50
8
38 Find the square root of 1764 by the Prime Factorisation Method. 8
39 Find the square of 86 without multiplication. 8
40 Find the square of the following
numbers using the identity ( (a+b)^{2}= )
( a^{2}+2 a b+b^{2}: )
( mathbf{2 0 9} )
8
41 Find the square root of 0.1764
A . 0.42
B. 0.46
c. 0.48
D. 0.49
8
42 If aabb is a four digit number and also a perfect square then the value of ( a+b ) is
A . 12
B. 11
c. 10
D. 9
8
43 51. If 33 = 5.745, then the val-
is approximately
(1) 1
(3) 6.32
(2) 0.5223
(4) 2.035
8
44 4. Calculate
26 correct to two places of decimal.
8
45 Use identities to evaluate : ( (502)^{2} )
A .1,62,004
в. 1,22,004
c. 2,12,004
D. 2,52,004
8
46 Find the square root of a given number by the prime factorization method. 529 8
47 ( mathbf{f} mathbf{3}^{x+1}=mathbf{9}^{x-2}, ) find the value of ( mathbf{2}^{1+x} ) 8
48 Find the square root of:
( mathbf{3 1}+mathbf{4} sqrt{mathbf{2 1}} )
A. ( sqrt{24}+sqrt{3} )
В. ( sqrt{28}+sqrt{3} )
c. ( sqrt{36}+sqrt{3} )
D. ( sqrt{28}+sqrt{2} )
8
49 Square of a ………….. number between 0 and 1 is …….
than the number itself.
6151
8
50 Evaluate the following
( (0.98)^{2} )
A .0 .9664
B. 0.9604
( c .0 .9864 )
D. 0.9964
8
51 Find out the following squares by using the identities:
( left(x-frac{1}{x}right)^{2} )
8
52 Find the square root of 12.25 using long division method.
A . 3.2
в. 3.4
( c .3 .5 )
D. ( 3 . )
8
53 2.
The number of zeroes at the end of the square of a number
is ………….. the number of zeroes at the end of the number.
The square root of a 4 digitor a 3 digit number is a
8
54 5.
A
A number ending in an odd number of zeros is never a
perfect square.
8
55 Simplify: ( (2) frac{1}{4} .(4)^{frac{1}{8}} .(8) frac{1}{16} .(16)^{frac{1}{32}} ) 8
56 A square yard has area ( 1764 mathrm{m}^{2} ). From a
corner of this yard, another square part
of area ( 784 mathrm{m}^{2} ) is taken out for public
utility. The remaining portion is divided in to 5 equal square parts. What is the perimeter of each of these equal parts?
8
57 If ( a^{x}=b^{y}=c^{z} ) and ( b^{2}=a c, ) then show
that ( boldsymbol{y}=frac{boldsymbol{2} boldsymbol{z} boldsymbol{x}}{boldsymbol{z}+boldsymbol{x}} )
8
58 A number whose square root is exact is called a ….
Lumber of zeroes at the end of a nerfect mare is olun
8
59 For a given number, find the smallest whole number by which it should be
divided so as to get a perfect square. 2925
8
60 Find the square root of the following number by factorisation.
( mathbf{1 9 6} )
8
61 A square garden has area 24686.6944
( m^{2} . ) A trench of one meter wide has to be
dug along the boundary inside the garden. After digging the trench, what will be the area of the left out garden?
8
62 Find the value of ( sqrt{49} ) 8
63 Simplify:
( (a+b+c)^{2}-(a-b+c)^{2} )
8
64 Evaluating the following:
( (1+2 sqrt{x})^{5}+(1-2 sqrt{x})^{5} )
A ( cdot 2left(1+40 x^{2}+80 xright) )
B. ( 2left(1-40 x+81 x^{2}right) )
c. ( 2left(1+40 x+80 x^{2}right) )
D. None of these
8
65 Svical triplet is (0, 35, 37).
ind the smallest number by which 252 must be multiplied so that the product becomes a perfect square. Also find the square
root of the perfect square so obtained.
Sol. Writing 252 as product of its prime factors, we get
8
66 Multiply:
( (a b+b c+c a) ) by ( (a b-b c-c a) )
8
67 Find the square of the following
numbers using the identity ( (a-b)^{2}= )
( a^{2}-2 a b+b^{2}: )
( mathbf{9 9} )
8
68 Expand ( (5-6 sqrt{3})^{2} )
A. ( 133+30 sqrt{3} )
В. ( 133-60 sqrt{3} )
D. ( 83+30 sqrt{3} )
8
69 What is the value of ( sqrt{441} ? )
A . 20
в. 2
( c cdot 22 )
D. None of these
8
70 Find the square of the following number without multiplication.
46
A . 2116
B. 2002
c. 2424
D. 1988
8
71 Find the square root of following surds:
( mathbf{5}+sqrt{mathbf{2 1}} )
8
72 59.
Vio+425 +4208 + V154 + 1225
(1) 4
(38
(4)
8
73 Find the square root of the following
decimal fraction:
( mathbf{0 . 0 6 2 5} )
8
74 A man, after a tour, finds that he had
spent every day as many rupees as the number of days he had been on tour How long did his tour last, if he had
spent in all ( R s .1,296 ? )
8
75 Find the smallest number which when
subtracted from 9761 , the difference is
a perfect cube
8
76 Find the square root of 121 using repeated subtraction. 8
77 Write the following in the expanded
form:
( (x+2 y+4 z)^{2} )
8
78 Find the square root of the following number by Division method.
( mathbf{3 1 3 6} )
8
79 2.
JIJTITI+11+13+15+17+19+21+
Write pythagorean triplet whose one number is
(a) 8
(b) 12
8
80 2. Find the smallest square number which is divisible by each of
Sol. We know that smallest number which is
is divisible by each of the number 4, 6 and 12.
ch is divisible by each of the number 4,6, 12 is LCM(4, 6, 12)
8
81 Find the square root of 33453 8
82 If 72 = 49 and 0.72 = 0.49 then 0.0072 = 0.000049. 8
83 Evaluate each of the following using identities:
¡) ( (399)^{2} )
ii) ( (0.98)^{2} )
iii) ( 991 times 1009 )
A . i ) 159876 ì 0.9
iii) 876590
в. ¡ ¡) 135879
ii) 0.87
iii) 896750
( c cdot ) i) 15920
ii) 0.9604
iii) 999919
D. i) 138760
ii) 0.9
iii) 999999
8
84 The sum of the squares of 2 numbers is
156. If the one number is 5 , the square of the other number is
( mathbf{A} cdot 81 )
в. 131
c. 11
D. 123
8
85 ( sqrt{0.01}+sqrt{0.0064}=? )
A . 0.3
B. 0.03
c. ( sqrt{0.18} )
D. None of these
8
86 f ( 2 x+3 y=8 ) and ( x y=2, ) find the
value of ( 4 x^{2}+9 y^{2} )
8
87 Find the square root of the following number by the prime factorisation method.
4356
8
88 Determine ( (8 x)^{x}, ) if ( 9^{x+2}=240+9^{x} ) 8
89 Find the square of 43 without multiplication.
A . 2401
в. 4801
( c .1842 )
D. 1849
8
90 1.
How do we find the square root of a fraction?
_
1
8
91 Solve: ( sqrt{225} ) 8
92 The value of ( sqrt{5+sqrt{11+sqrt{19+sqrt{20+sqrt{49}}}}} )
simplifying is
( A )
B. 2
( c cdot 4 )
( D )
8
93 Square root of 375 is – 8
94 Solve: ( sqrt{e^{4 x}-e^{2 x}} ) 8
95 17.
it
c
……….
The number of zeroes at the end of a perfect square is always
7.
……. NDOS
nyo
S
nhs.OSONA
NYT
8
96 By splitting into prime factors, find the
square root of:
194481
8
97 Expand each of the following, using suitable identities:
( (x+2 y+4 z)^{2} )
8
98 2.
1 – 49 alu U./ = . m v.
v.v .
The square of a proper fraction is always greater than itself.
TL. nararaat af anrime number can be obtained
4
8
99 Find the square root of the following number by Division method.
( mathbf{7 9 2 1} )
8
100 Find the square root of the following number by division method: 5329 8
101 By splitting into prime factors, find the
square root of 11025
A. 1005
в. 105
c. 100
D. 115
8
102 If ( x^{2}+frac{1}{x^{2}}=1022, ), then find ( x+frac{1}{x} ) 8
103 Find the square root of 298116 by prime factorization.
1.
8
104 2.
Is 3 the square of any rational number?
8
105 Expand each of the following, using suitable identities:
( (-2 x+5 y-3 z)^{2} )
8
106 Simplify the following expressions:
( left(x^{2}-x+1right)^{2}-left(x^{2}+x+1right)^{2} )
8
107 Find the square root of 298116 using
long division method.
A . 546
в. 123
c. 234
D. 564
8
108 13. Find the least square number exactly divisible by each of
the number 6,5,10 and 20.
8
109 Find the square of ( 3 a+7 b )
( mathbf{A} cdot 9 a^{2}+42 a b+49 b^{2} )
B ( cdot 9 a^{2}+40 a b+49 b^{2} )
C ( cdot 18 a^{2}+42 a b+98 b^{2} )
D. ( 18 a^{2}+40 a b+98 b^{2} )
8
110 Find the square of 83 without actual multiplication
A . 6880
B. 3881
( c .3889 )
D. 6889
8
111 ( sqrt{3}+2 sqrt{2}+sqrt{3-2 sqrt{2}}=dots ? )
A ( cdot 2+2 sqrt{2} )
B. ( 2 sqrt{2} )
c. 1
D.
8
112 Find the square root of:
0.602 correct to two places of decimal
8
113 Find the sum of square of the following
number:
( mathbf{3 9} )
8
114 If ( boldsymbol{x}=mathbf{3}-mathbf{2} sqrt{mathbf{2}}, ) find ( boldsymbol{x}^{4}+frac{mathbf{1}}{boldsymbol{x} mathbf{4}} ? ) 8
115 V
ol-2.
Find the smallest number by which 15552 must be divided so that it becomes a perfect square. Also find the squar
perfect square number.
I. By writing 15552 as product of its prime factors we get
8
116 Find the square root of a number 529 by Prime Factorisation Method. 8
117 ( 63 div sqrt{0.0049} ) equals
A . 1.285
B. 900
( c cdot 90 )
D. 12.85
8
118 M
+
N

9.
If x and y are two positive numbers, then
Put = or # in the given boxes.
1 xx ſ ry
VO
+
y
(7) Sx + 7
(iv) VX-7
o 8x + √
dx – sy
8
119 Find the square of ( a+2 b+c )
( mathbf{A} cdot a^{2}+b^{2}+c^{2}+a b+b c+a c )
B ( cdot a^{2}+4 b^{2}+c^{2}+4 a b+4 b c+2 a c )
C ( cdot a^{3}+4 b^{3}+c^{3}+8 a b+8 b c+8 a c )
D. ( a^{3}+b^{3}+c^{3}+4 a b+4 b c+2 a c )
8
120 Find the square root of the following number by division method: 28224 8
121 Without actual finding the square of the numbers, find the value of ( 36^{2}-35^{2} )
A . 70
B. 71
( c cdot 72 )
D. 73
8
122 If ( 3^{4 x}=(81)^{-1} ) and ( 10^{1 / y}=0.0001, ) find
the value of ( 2^{-x+4 y} )
8
123 6.
Square of a prime number is always prime.
8
124 Find the square root of ( left(boldsymbol{x}+frac{1}{boldsymbol{x}}right)^{2} )
( 4left(x-frac{1}{x}right) )
8
125 How many factors of 1080 a
A .32
B. 36
c. 8
D. 25
8
126 Find the square root of 256 8
127 Find the square root of 4489 by Division
method.
8
128 If ( a^{2}+frac{1}{a^{2}}=102, ) find the value of ( a-frac{1}{a} ) 8
129 2.
Column-II
(p) 324
(q) 64
Column-I
A. If (75.24+ x) = 8.71
then the value of x is
B. If 0.04×0.4x a
0.4 x 0.04 x 6
then the value of is
if 256 + Vx = 2 then the
value of x is
C
(1) 0.016
54
D. If V16939
X =
then
(5) .6241
the value of x is
8
130 3.
The square root of a 4-digit or a 3 digit number is a ……..
digit number.
number between 0 and 1 is
8
131 Find the square of the following
numbers using the identity ( (a-b)^{2}= )
( a^{2}-2 a b+b^{2}: )
( mathbf{9 9 9} )
8
132 Find the square root of the following numbers using division method:
0.431649
8
133 Evaluate:
( left(153^{2}right)-left(147^{2}right) ? )
8
134 Expand each of the following, using suitable identities:
( (-2 x+3 y+2 z)^{2} )
8
135 8.
A perfect square leaves a remainder 0 or 1, by dividing with
8
136 The square root of a perfect square containing ‘n’ digits has …………… digits.
A ( cdot frac{n+1}{2} )
в. ( frac{n}{2} )
c. A or B
D. None of these
8
137 Find the square root of the following number by the prime factorisation method. ( mathbf{6} frac{mathbf{1}}{mathbf{4}} ) 8
138 14. Evaluate. V1.96.
15. Find the value of 45 x 20.
8
139 51. If 33 = 5.745, then the val-
3
ue of 1
is approximately
(1) 1
(3) 6.32
(2) 0.5223
(4) 2.035
8
140 Find the square root of 841
A . 2
B. 28
( c cdot 29 )
D. 25
8
141 Evaluate the following products without multiplying directly:
( mathbf{1 0 4} times mathbf{9 6} )
8
142 Find the square of 125
A .84113
B . 48000
c. 15625
D. 84920
8
143 Find the square roots of the given number by Prime factorization method: 441 8
144 State whether true or false:
Square root of 121 is 11 and (-11)
A. True
B. False
8
145 Find the square root of 2002225 8
146 The value of ( sqrt{10+sqrt{25+sqrt{108+sqrt{154+sqrt{225}}}}} )
is:
A . 4
B. 6
( c cdot 8 )
D. 10
8
147 What is the value of ( sqrt{7.84}+ ) ( sqrt{0.0784}+sqrt{0.000784}+sqrt{0.00000784} )
( ? )
A . 3.08
B. 3.108
c. 3.1008
D. 3.1108
8
148 Find the square root of 125 using repeated subtraction. 8
149 Evaluate the following
( (97)^{2} )
A. 9409
в. 9049
( c .9949 )
D. 4949
8
150 Simplify:
( (a+b+c)^{2}+(a-b+c)^{2} )
8
151 Find square root of 0.4225
A . 0.65
B. 6.5
c. 0.21
D. 0.021
8
152 ( sqrt{3}+2 sqrt{2}-sqrt{3}-2 sqrt{2} ) is equal to
A . 2
B.
( c cdot 2 sqrt{2} )
D. ( sqrt{6} )
8
153 If ( boldsymbol{x}-frac{mathbf{1}}{boldsymbol{x}}=sqrt{mathbf{6}}, ) then ( boldsymbol{x}^{2}+frac{mathbf{1}}{boldsymbol{x}^{2}} ) is
( A cdot 2 )
B. 4
( c cdot 6 )
D.
8
154 7. V625 +/484
(1) 57
(3) 35
(2) 37
(4) 47
8
155 ( x^{2}-256=0 ) find ( x ) 8
156 Use prime factorisation to find the square root of 1225
A . 122
в. 225
c. 35
D. 50
8
157 3.
Find the square root of
(1) 480249
(ii) 0.00008281
8
158 4.
Without adding find the sum :
1+3+5+7+9+11+13+15+17+19
8
159 What is the square root of 506.25 using long division method?
A . 22.
B. 21.4
c. 23.4
D. 25.3
8
160 2.
Find the value of
(1) 199 x 1396
(ü)
147 x 243
8
161 If ( x=(2+sqrt{5})^{1 / 2}+(sqrt{5}-2)^{1 / 2} ) and
( y=(2+sqrt{5})^{1 / 2}-(sqrt{5}-2)^{1 / 2} ), then
evaluate ( x^{2}+y^{2} ).
8
162 Using identities, find the square of 101 8
163 Some equations are solved on the basis
of a certain system. Find the correct
answer for the unsolved equation on that basis. If ( 324 times 289=35,441 times )
( mathbf{4 8 4}=mathbf{4 3}, mathbf{6 2 5} times mathbf{4 0 0}=mathbf{4 5}, ) find the
value of ( 256 times 729 )
A . 33
B . 35
c. 43
D. 34
8
164 12. Find the square of the number 509 using the identity
(a + b)2 = a + 2ab + b2.
8
165 For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number
2028
8
166 Find the square root of the following number by the prime factorisation method
( mathbf{1 9 3 6} )
8
167 Without adding, find the sum,
(a) 1+3+5+7+9+11+13+15+17+19
(b) 1+3+5+7+9+11+13+15+17+19+21+ 23
1*3*5*7*9***1315*17*+21+22
8
168 6.
Square of a prime number is always prime.
8
169 Find square root of ( x=sqrt{20.25} ) 8
170 74. If 16 is divided into two parts
so that twice the square of
larger part is 164 more than
the square of smaller part,
then the value of larger part
will be
(1) 6
(3) 10 (4) 12
(2) 8
8
171 f ( a=2 ) and ( b=3, ) then find the values
of each of the following: ( (a+b)^{a} )
8
172 Find the following squares by using the identity ( left(frac{2 a}{3 b}+frac{3 b}{2 a}right)^{2} ) 8
173 Write down the values of:
( (sqrt{5}+sqrt{6})^{2} )
A. ( sqrt{5}+sqrt{6}+sqrt{30} )
B. ( 11+2 sqrt{30} )
c. ( 11+sqrt{30} )
D. ( sqrt{11}+60 )
8
174 Find the square root of 7744 by the division method.
( mathbf{A} cdot 82 )
B. 88
c. 92
D. 98
8
175 Find the square root of each of the
following by prime factorization:
( mathbf{1 1 6 6 4} )
8
176 The following expression is a rational number. Find its value. ( sqrt[3]{mathbf{6} sqrt{mathbf{3}}+mathbf{1 0}}-sqrt[3]{mathbf{6} sqrt{mathbf{3}}-mathbf{1 0}} ) 8
177 Evaluating the following:
( (sqrt{3}+1)^{5}-(sqrt{3}-1)^{5} )
8
178 17. A man walks 30 km tov
South and turns left and
walks 50 km. Then he w
10 km North before he tal
left to walk 50 km. How f
he from the original place
(1) 10 km (2) 20 km
(3) 30 km (4) O km
m towards
ft and and
n he walks
he takes a
How far is
8
179 Calculate: ( sqrt{4} ) 8
180 Without actual finding the square of the numbers, find the value of ( 120^{2}-119^{2} )
A . 239
в. 240
( c cdot 238 )
D. 237
8
181 Find the consecutive perfect squares
between which the following numbers
lie: 123456
8
182 Find the square of the following
numbers using the identity ( (a+b)^{2}= )
( a^{2}+2 a b+b^{2}: )
510
8
183 Find the square root of -625 ( (sqrt{-1}=i) )
( mathbf{A} cdot mathbf{5} )
B. -5
( c .25 i )
D. -25
8
184 If ( a+b+c=6 ) and ( a b+b c+c a=11 )
Find ( left(a^{2}+b^{2}+c^{2}right) ? )
A . 14
B . 25
( c cdot 36 )
D. 47
8
185 Find the square of the following
numbers using the identity ( (a-b)^{2}= )
( a^{2}-2 a b+b^{2}: )
495
8
186 The “geocenter” of two positive numbers is defined as the positive square root of their product. If the geocenter of 5 and ( x )
is ( 9, ) calculate the value of ( x )
A . 6.7
в. 7.0
c. 11.3
D. 13.0
E . 16.2
8
187 Find square of the following expression ( frac{3 a}{2 b}-frac{2 b}{3 a} )
A ( cdot frac{9 a^{2}}{4 b^{2}}-2+frac{b^{2}}{a^{2}} )
в. ( frac{9 a^{2}}{4 b^{2}}+2+frac{4 b^{2}}{9 a^{2}}^{2} )
c. ( frac{a^{2}}{4 b^{2}}-2+frac{4 b^{2}}{9 a^{2}} )
D. ( frac{9 a^{2}}{4 b^{2}}-2+frac{4 b^{2}}{9 a^{2}} )
8
188 Write the following in the expanded
form:
( (2 x-y+z)^{2} )
8
189 Evaluate: ( left{left(5^{2}+12^{2}right)^{frac{1}{2}}right} 3 )
A . 54
B. 34
c. 39
D. 59
8
190 (0.05)2 + (0.41)2 + (0.073)2
54.
(0.0052 + (2041)2 + (0.00732 Is
(1) 10 (2) 100
(3) 1000
(4) None of these
8
191 An odd number when multiplied by itself gives 2401. Find
the number.
8
192 If ( x+frac{1}{x}=4, ) then ( x^{4}+frac{1}{x^{4}} ) is equal to
A . 196
B. 194
( c .192 )
D. 19
8
193 8. Find the least number of four digits which is a perfect square.
Sol. Least number of 4 digits is 1000, it is not perfect square.
8
194 If ( boldsymbol{x}=mathbf{9}+mathbf{4} sqrt{mathbf{5}} ) then ( sqrt{boldsymbol{x}}-frac{mathbf{1}}{sqrt{boldsymbol{x}}} ) is equal
to?
8
195 Find the least number by which 384
must be divided to make it a perfect
square
8
196 On simplification the product of given expression ( left(x-frac{1}{x}right)left(x+frac{1}{x}right)left(x^{2}+frac{1}{x^{2}}right) )
A ( cdot x^{3}-frac{1}{x^{3}} )
в. ( x^{3}+frac{1}{x^{3}} )
c. ( x^{4}-frac{1}{x^{4}} )
D. ( x^{4}+frac{1}{x^{4}} )
8
197 53. If 4096 = 64, then the value
of 40.96 + 10.4096 +
0.004096 +70.00004096
up to two places of decimals is :
(1) 7.09 (2) 7.10
(3) 7.11 (4) 7.12
8
198 Find the square root of ( 1024 . ) Hence find the value of ( sqrt{10.24}+sqrt{0.1024}+ )
( sqrt{10240000} )
8
199 Expression the following as the product of expression through prime factorization
( mathbf{2 8 8} )
8
200 3.
The square root of a prime number can be obtained
approximately but not exactly.
8
201 Find the square of the following numbers without actual multiplication
( mathbf{3 9} )
8
202 If ( 3 x-frac{1}{2 x}=6, ) then the value of ( 9 x^{2}+ )
( frac{1}{4 x^{2}} )
A . 36
B. 33
c. 30
D. 39
8
203 If ( sin theta-operatorname{cosec} theta=sqrt{5}, ) then the value of
( sin theta+operatorname{cosec} theta ) is:
A. ( sqrt{3} )
B.
( c cdot 3 )
D.
8
204 The value of ( sqrt{214+sqrt{130-sqrt{88-sqrt{44+sqrt{25}}}}} )
A . 14
B. 15
c. 16
D. 17
8

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