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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