# 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 NoQuestionsClass
1Write the following in the expanded
form:
( (m+2 n-5 p)^{2} )
8
2Find 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
314. Evaluate: 11.96.8
4If ( 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
5For 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
6Find the smallest whole number by
which 252 should be divided, so as to
get a perfect square.
8
74.
The square of an odd number is always odd.
V
*
*
mir
ou Foque PP a
8
812.
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
95.
If’a’ is a square root of ‘b’ then ‘b’is ………….. of‘a’.
6
A number whose sauare root is avant in animda
8
10If ( 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
12Find the square root of the following numbers by the factorisation numbers:
82944
8
13Use identities to evaluate ( (mathbf{9 7})^{2} )
A. 9,109
B. 9,409
c. 9,909
D. 9,209
8
14Find the following squares by using the identity
( left(frac{x^{2}}{y z}+frac{y^{2}}{x z}right)^{2} )
8
15Use 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
1610. If (2 x 9) (2 x 9) is 324, then find the value of
324.
8
1765. 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
18By splitting into prime factors, find the square root of 729
A . 27
B. 21
c. 17
D. 87
8
19By using identity.
( (mathbf{7} 99)^{2}=? )
8
20What is ten times the square root of the
following decimal number:
( mathbf{7 . 2 9} )
8
21Find the square root of the following number by Division method.
( mathbf{1 3 6 9} )
8
226.
How many natural numbers lie between squares of 12
and 13.
8
23Simplify:
( (boldsymbol{a}+boldsymbol{b}+boldsymbol{c})^{2}+(boldsymbol{a}-boldsymbol{b}+boldsymbol{c})^{2}+ )
( (a+b-c)^{2} )
8
24Evaluate the following by using the
identities:
( 48^{2} )
8
25The 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
26Evaluate ( left(17^{2}-8^{2}right)^{frac{1}{2}} )8
27Evaluate: ( sqrt{mathbf{1 0 0}}+sqrt{mathbf{4 9}} )
A. ( sqrt{149} )
B. ( sqrt{490} )
c. ( sqrt{10}+sqrt{14} )
D. 17
8
28Find 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
29DU, 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
30Find the squares of 510 using the identity
( (a+b)^{2}=a^{2}+2 a b+b^{2} )
8
31Find the square root of 13.31 using long
division method.
8
32Express 49 as the sum of 7 odd natural numbers.
1
1:.
1.
.
8
33Square numbers can only have………….. number of zeros a
the end.
The number of merced at the end of the square of a numbe
8
34Find 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
36Evaluate ( 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
37Find 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
38Find the square root of 1764 by the Prime Factorisation Method.8
39Find the square of 86 without multiplication.8
40Find the square of the following
numbers using the identity ( (a+b)^{2}= )
( a^{2}+2 a b+b^{2}: )
( mathbf{2 0 9} )
8
41Find the square root of 0.1764
A . 0.42
B. 0.46
c. 0.48
D. 0.49
8
42If 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
4351. If 33 = 5.745, then the val-
is approximately
(1) 1
(3) 6.32
(2) 0.5223
(4) 2.035
8
444. Calculate
26 correct to two places of decimal.
8
45Use identities to evaluate : ( (502)^{2} )
A .1,62,004
в. 1,22,004
c. 2,12,004
D. 2,52,004
8
46Find the square root of a given number by the prime factorization method. 5298
47( mathbf{f} mathbf{3}^{x+1}=mathbf{9}^{x-2}, ) find the value of ( mathbf{2}^{1+x} )8
48Find 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
49Square of a ………….. number between 0 and 1 is …….
than the number itself.
6151
8
50Evaluate the following
( (0.98)^{2} )
A .0 .9664
B. 0.9604
( c .0 .9864 )
D. 0.9964
8
51Find out the following squares by using the identities:
( left(x-frac{1}{x}right)^{2} )
8
52Find the square root of 12.25 using long division method.
A . 3.2
в. 3.4
( c .3 .5 )
D. ( 3 . )
8
532.
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
545.
A
A number ending in an odd number of zeros is never a
perfect square.
8
55Simplify: ( (2) frac{1}{4} .(4)^{frac{1}{8}} .(8) frac{1}{16} .(16)^{frac{1}{32}} )8
56A 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
57If ( 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
58A number whose square root is exact is called a ….
Lumber of zeroes at the end of a nerfect mare is olun
8
59For a given number, find the smallest whole number by which it should be
divided so as to get a perfect square. 2925
8
60Find the square root of the following number by factorisation.
( mathbf{1 9 6} )
8
61A 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
62Find the value of ( sqrt{49} )8
63Simplify:
( (a+b+c)^{2}-(a-b+c)^{2} )
8
64Evaluating 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
65Svical 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
66Multiply:
( (a b+b c+c a) ) by ( (a b-b c-c a) )
8
67Find the square of the following
numbers using the identity ( (a-b)^{2}= )
( a^{2}-2 a b+b^{2}: )
( mathbf{9 9} )
8
68Expand ( (5-6 sqrt{3})^{2} )
A. ( 133+30 sqrt{3} )
В. ( 133-60 sqrt{3} )
D. ( 83+30 sqrt{3} )
8
69What is the value of ( sqrt{441} ? )
A . 20
в. 2
( c cdot 22 )
D. None of these
8
70Find the square of the following number without multiplication.
46
A . 2116
B. 2002
c. 2424
D. 1988
8
71Find the square root of following surds:
( mathbf{5}+sqrt{mathbf{2 1}} )
8
7259.
Vio+425 +4208 + V154 + 1225
(1) 4
(38
(4)
8
73Find the square root of the following
decimal fraction:
( mathbf{0 . 0 6 2 5} )
8
74A 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
75Find the smallest number which when
subtracted from 9761 , the difference is
a perfect cube
8
76Find the square root of 121 using repeated subtraction.8
77Write the following in the expanded
form:
( (x+2 y+4 z)^{2} )
8
78Find the square root of the following number by Division method.
( mathbf{3 1 3 6} )
8
792.
JIJTITI+11+13+15+17+19+21+
Write pythagorean triplet whose one number is
(a) 8
(b) 12
8
802. 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
81Find the square root of 334538
82If 72 = 49 and 0.72 = 0.49 then 0.0072 = 0.000049.8
83Evaluate 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
84The 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
86f ( 2 x+3 y=8 ) and ( x y=2, ) find the
value of ( 4 x^{2}+9 y^{2} )
8
87Find the square root of the following number by the prime factorisation method.
4356
8
88Determine ( (8 x)^{x}, ) if ( 9^{x+2}=240+9^{x} )8
89Find the square of 43 without multiplication.
A . 2401
в. 4801
( c .1842 )
D. 1849
8
901.
How do we find the square root of a fraction?
_
1
8
91Solve: ( sqrt{225} )8
92The value of ( sqrt{5+sqrt{11+sqrt{19+sqrt{20+sqrt{49}}}}} )
simplifying is
( A )
B. 2
( c cdot 4 )
( D )
8
93Square root of 375 is –8
94Solve: ( sqrt{e^{4 x}-e^{2 x}} )8
9517.
it
c
……….
The number of zeroes at the end of a perfect square is always
7.
……. NDOS
nyo
S
nhs.OSONA
NYT
8
96By splitting into prime factors, find the
square root of:
194481
8
97Expand each of the following, using suitable identities:
( (x+2 y+4 z)^{2} )
8
982.
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
99Find the square root of the following number by Division method.
( mathbf{7 9 2 1} )
8
100Find the square root of the following number by division method: 53298
101By splitting into prime factors, find the
square root of 11025
A. 1005
в. 105
c. 100
D. 115
8
102If ( x^{2}+frac{1}{x^{2}}=1022, ), then find ( x+frac{1}{x} )8
103Find the square root of 298116 by prime factorization.
1.
8
1042.
Is 3 the square of any rational number?
8
105Expand each of the following, using suitable identities:
( (-2 x+5 y-3 z)^{2} )
8
106Simplify the following expressions:
( left(x^{2}-x+1right)^{2}-left(x^{2}+x+1right)^{2} )
8
107Find the square root of 298116 using
long division method.
A . 546
в. 123
c. 234
D. 564
8
10813. Find the least square number exactly divisible by each of
the number 6,5,10 and 20.
8
109Find 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
110Find 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
112Find the square root of:
0.602 correct to two places of decimal
8
113Find the sum of square of the following
number:
( mathbf{3 9} )
8
114If ( boldsymbol{x}=mathbf{3}-mathbf{2} sqrt{mathbf{2}}, ) find ( boldsymbol{x}^{4}+frac{mathbf{1}}{boldsymbol{x} mathbf{4}} ? )8
115V
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
116Find 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
118M
+
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
119Find 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
120Find the square root of the following number by division method: 282248
121Without 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
122If ( 3^{4 x}=(81)^{-1} ) and ( 10^{1 / y}=0.0001, ) find
the value of ( 2^{-x+4 y} )
8
1236.
Square of a prime number is always prime.
8
124Find the square root of ( left(boldsymbol{x}+frac{1}{boldsymbol{x}}right)^{2} )
( 4left(x-frac{1}{x}right) )
8
125How many factors of 1080 a
A .32
B. 36
c. 8
D. 25
8
126Find the square root of 2568
127Find the square root of 4489 by Division
method.
8
128If ( a^{2}+frac{1}{a^{2}}=102, ) find the value of ( a-frac{1}{a} )8
1292.
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
1303.
The square root of a 4-digit or a 3 digit number is a ……..
digit number.
number between 0 and 1 is
8
131Find the square of the following
numbers using the identity ( (a-b)^{2}= )
( a^{2}-2 a b+b^{2}: )
( mathbf{9 9 9} )
8
132Find the square root of the following numbers using division method:
0.431649
8
133Evaluate:
( left(153^{2}right)-left(147^{2}right) ? )
8
134Expand each of the following, using suitable identities:
( (-2 x+3 y+2 z)^{2} )
8
1358.
A perfect square leaves a remainder 0 or 1, by dividing with
8
136The 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
137Find the square root of the following number by the prime factorisation method. ( mathbf{6} frac{mathbf{1}}{mathbf{4}} )8
13814. Evaluate. V1.96.
15. Find the value of 45 x 20.
8
13951. 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
140Find the square root of 841
A . 2
B. 28
( c cdot 29 )
D. 25
8
141Evaluate the following products without multiplying directly:
( mathbf{1 0 4} times mathbf{9 6} )
8
142Find the square of 125
A .84113
B . 48000
c. 15625
D. 84920
8
143Find the square roots of the given number by Prime factorization method: 4418
144State whether true or false:
Square root of 121 is 11 and (-11)
A. True
B. False
8
145Find the square root of 20022258
146The value of ( sqrt{10+sqrt{25+sqrt{108+sqrt{154+sqrt{225}}}}} )
is:
A . 4
B. 6
( c cdot 8 )
D. 10
8
147What 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
148Find the square root of 125 using repeated subtraction.8
149Evaluate the following
( (97)^{2} )
A. 9409
в. 9049
( c .9949 )
D. 4949
8
150Simplify:
( (a+b+c)^{2}+(a-b+c)^{2} )
8
151Find 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
153If ( 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
1547. V625 +/484
(1) 57
(3) 35
(2) 37
(4) 47
8
155( x^{2}-256=0 ) find ( x )8
156Use prime factorisation to find the square root of 1225
A . 122
в. 225
c. 35
D. 50
8
1573.
Find the square root of
(1) 480249
(ii) 0.00008281
8
1584.
Without adding find the sum :
1+3+5+7+9+11+13+15+17+19
8
159What is the square root of 506.25 using long division method?
A . 22.
B. 21.4
c. 23.4
D. 25.3
8
1602.
Find the value of
(1) 199 x 1396
(ü)
147 x 243
8
161If ( 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
162Using identities, find the square of 1018
163Some 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
16412. Find the square of the number 509 using the identity
(a + b)2 = a + 2ab + b2.
8
165For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number
2028
8
166Find the square root of the following number by the prime factorisation method
( mathbf{1 9 3 6} )
8
(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
1686.
Square of a prime number is always prime.
8
169Find square root of ( x=sqrt{20.25} )8
17074. 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
171f ( a=2 ) and ( b=3, ) then find the values
of each of the following: ( (a+b)^{a} )
8
172Find the following squares by using the identity ( left(frac{2 a}{3 b}+frac{3 b}{2 a}right)^{2} )8
173Write 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
174Find the square root of 7744 by the division method.
( mathbf{A} cdot 82 )
B. 88
c. 92
D. 98
8
175Find the square root of each of the
following by prime factorization:
( mathbf{1 1 6 6 4} )
8
176The following expression is a rational number. Find its value. ( sqrt{mathbf{6} sqrt{mathbf{3}}+mathbf{1 0}}-sqrt{mathbf{6} sqrt{mathbf{3}}-mathbf{1 0}} )8
177Evaluating the following:
( (sqrt{3}+1)^{5}-(sqrt{3}-1)^{5} )
8
17817. 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
179Calculate: ( sqrt{4} )8
180Without 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
181Find the consecutive perfect squares
between which the following numbers
lie: 123456
8
182Find the square of the following
numbers using the identity ( (a+b)^{2}= )
( a^{2}+2 a b+b^{2}: )
510
8
183Find the square root of -625 ( (sqrt{-1}=i) )
( mathbf{A} cdot mathbf{5} )
B. -5
( c .25 i )
D. -25
8
184If ( 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
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185Find the square of the following
numbers using the identity ( (a-b)^{2}= )
( a^{2}-2 a b+b^{2}: )
495
8
186The “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
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187Find 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}} )
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188Write the following in the expanded
form:
( (2 x-y+z)^{2} )
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189Evaluate: ( left{left(5^{2}+12^{2}right)^{frac{1}{2}}right} 3 )
A . 54
B. 34
c. 39
D. 59
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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
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191An odd number when multiplied by itself gives 2401. Find
the number.
8
192If ( x+frac{1}{x}=4, ) then ( x^{4}+frac{1}{x^{4}} ) is equal to
A . 196
B. 194
( c .192 )
D. 19
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1938. 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
194If ( boldsymbol{x}=mathbf{9}+mathbf{4} sqrt{mathbf{5}} ) then ( sqrt{boldsymbol{x}}-frac{mathbf{1}}{sqrt{boldsymbol{x}}} ) is equal
to?
8
195Find the least number by which 384
must be divided to make it a perfect
square
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196On 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}} )
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19753. 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
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198Find the square root of ( 1024 . ) Hence find the value of ( sqrt{10.24}+sqrt{0.1024}+ )
( sqrt{10240000} )
8
199Expression the following as the product of expression through prime factorization
( mathbf{2 8 8} )
8
2003.
The square root of a prime number can be obtained
approximately but not exactly.
8
201Find the square of the following numbers without actual multiplication
( mathbf{3 9} )
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202If ( 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
203If ( 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
204The 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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