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Square Root And Cube Root Quiz For SSC CGL 2018

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Square Root And Cube Root Quiz For SSC CGL 2018

Square Root And Cube Root Quiz For SSC CGL 2018

Q1. The number of digits in the square root of 625686734489 is

(a) 4

(b) 5

(c) 6

(d) 7

Answer: (c)

Explanation :

The number of digits in 625686734489 is 12. ; :: Number of digits in its square root = 6

i.e.  1

Q2. If (1101)2 = 1212201, find the value of  2

(a) 110.1

(b) 11.01

(c) 1.101

(d) 11.001

Answer: (b)

Explanation :

2

Q3. The smallest number added to 680621 to make the sum a perfect square is:

(a) 4

(b) 5

(c) 6

(d) 8

Answer: (a)

Explanation :

3

Q4. The digit in the unit’s place in the square-root of 15876 is:

(a) 8

(b) 6

(c) 4

(d) 2

Answer: (b)

Explanation :

15876 =126 ; The digit at the unit’s place is 6, illustration:

Q5. If(10.15)2 = 103.0225, then the value of 5is

(a) 1025.15

(b) 103.515

(c) 102.515

(d) 102.0515

Answer: (c)

Explanation :

5c

Q6. If (102)2 = 10404 then, the value of 5 is equal to

(a) 0.306

(b) 0.0306

(c) 11.122

(d) 11.322

Answer: (d)

Explanation :

7b

Q7. The smallest number which should be added to the number 8958 so that the result is a perfect square is

(a) 69

(b) 67

(c) 77

(d) 79

Answer: (b)

Explanation :

Now, 95 × 95=9025 ; :: Required number = 9025 – 8958 = 67

Q8. If 8 = 64, then value of 8 up to two places of decimals is:

(a) 7.09

(b) 7.10

(c) 7.11

(d) 7.12

Answer: (c)

Explanation :

8c

Q9. The sum of a positive integer and its square is 2450. The positive integer is

(a) 45

(b) 48

(c) 49

(d) 50

Answer: (c)

Explanation :

X2 + x = 2450 ; → x (x + 1) = 2450 = 49 ×50;

:: x = 49.

Q10. Which smallest number must be added to 2203 so that we get a perfect square?

(a) 1

(b) 3

(c) 6

(d) 8

Answer: (c)

Explanation : 47 × 47 = 2209; Clearly, 6 should be added to 2203 to get a perfect square.

Q11. The missing digit (•) in 1276•, so that the number is a perfect square, is

(a) 1

(b) 4

(c) 8

(d) 9

Answer: (d)

Explanation :

11

Clearly 9 should replace *

Q12. The number of perfect square numbers between 50 and 1000 is

(a) 21

(b) 22

(c) 23

(d) 24

Answer: (d)

Explanation :

Perfect square numbers between 50 and 1000 start from 64 to 961 i.e., (8)2 to (31)2

:: The required number = (31 – 8) + 1 = 24

Q13. The least integer which should be added to 1000 so as to make it a perfect square is

(a) 10

(b) 18

(c) 24

(d) 89

Answer: (c)

Explanation : (31)2 < 1000 M 322 ; 32 × 32=1024; :: = 1024 – 1000 = 24

Q14. The smallest number that must be subtracted from 1000 to make the resulting number a perfect square is

(a) 37

(b) 38

(c) 39

(d) 40

Answer: (c)

Explanation :

312 = 961; 322 = 1024; :: Required number= 1000 – 961 = 39

Q15. How many positive integers less than 1000 are multiples of 11 whose square roots are whole numbers.

(a) 2

(b) 4

(c) 8

(d) 11

Answer: (a)

Explanation :

Multiple of 11 whose square root are whole nu8mkber First = 11 =121 ; Second = 11

Q16. If the square root of 841 is 29. Then 0.00000841 to:

(a) 0.029

(b) 0.0029

(c) 0.00029

(d) 0.29

Answer: (b)

Explanation :

18cc

Q17. Given that 17=23.97, 19-2 = 75.8, then 19-1 equals to::

(a) 0.002397

(b)  0.0002397

(c) 0.007580

(d) 0.00758

Answer: (d)

Explanation :

19d

Q18. If 18 then value of x is:

(a) 1.64

(b) 2.64

(c) 1.764

(d) 0.1764

Answer: (d)

Explanation :

20d

Q19. How many perfect squares lie between 120 and 300?

(a) 5

(b) 6

(c) 7

(d) 8

Answer: (c)

Explanation :

112 = 121, 122 = 144 ; 132 = 169, 142 = 196 ; 152 225, 162 = 256.; 172 = 289 ; So, total perfect squares = 7

Q20. The smallest positive integer, when multiplied by 392,the product is a perfect square, is

(a) 6

(b) 5

(c) 3

(d) 2

Answer: (a)

Explanation : =

22

Clearly, 6 should be added to 2203 to get a  perfect square.

Q21. If cube root of 175616 is 56, then the value of 21is equal to:

(a) 0.168

(b) 62.16

(c) 6.216

(d) 6.116

Answer: (c)

Explanation :

1c

1cc

Q22. By what least number should 4320 be multiplied so as to obtain a number which is a perfect cube

(a) 40

(b) 50

(c) 60

(d) 80

Answer: (b)

Explanation :

22b

Q23. The smallest natural number, by which 3000 must be divided to make the quotient a perfect cube, is

(a) 3

(b) 4

(c) 5

(d) 6

Answer: (a)

Explanation : 3000 = 3 × 1000 = 3 × 103 ; Clearly, when we divide 3000 by natural number 3, the quotient is 1000 which is a perfect cube.

Q24. The least number, by which 1944 must, be multiplied so as to make the result a perfect cube, is

(a) 2

(b) 3

(c) 6

(d) 13

Answer: (b)

Explanation :

4b

Clearly, 1944 should be multiplied by 3 to make the result a perfect cube.

Q25. The least number that must be added to 1720 so as to obtain a perfect cube is

(a) 7

(b) 8

(c) 11

(d) 13

Answer: (b)

Explanation : 12 × 12 × 12 = 1728;

Required number = 1728 – 1720 = 8

Q26. Sum of digit of the smallest number by which 1440 be multiplied so that it becomes a perfect cube, is

(a) 4

(b) 6

(c) 7

(d) 8

Answer: (b)

Explanation :

26b

Q27. By which smallest number 1323 must be multiplied, so that it becomes a perfect cube?

(a) 2

(b) 3

(c) 5

(d) 7

Answer: (d)

Explanation :

17d

Q28. The smallest positive integer n, for which 864 n is a perfect cube, is:

(a) 1

(b) 2

(c) 3

(d) 4

Answer: (b)

Explanation :

28

28

Q29. Which smallest number must be added to 710 so that the sum is a perfect cube?

(a) 29

(b) 19

(c) 11

(d) 21

Answer: (b)

Explanation :

9b

Q30. By what least number should 675 be multiplied so as to obtain a perfect cube number?

(a) 3

(b) 5

(c) 24

(d) 40

Answer: (b)

Explanation :

10b

Q31. The sum of the squares of 2 numbers is 146 and the square root of one of them is √5. The cube of the other number is

(a) 1111

(b) 1221

(c) 1331

(d) 1441

Answer: (c)

Explanation :

11c

Q32. The least possible value of A for which 90 × A is a perfect cube is

(a) 200

(b) 300

(c) 500

(d) 600

Answer: (b)

Explanation :

12b

Q33. The square of a natural number subtracted from its cube is 48. The number is:

(a) 8

(b) 6

(c) 5

(d) 4

Answer: (d)

Explanation :

Let number be x  According to question x3 – x2 = 48

x = 4

Q34. 14 is equal to

(a) 0.5

(b) 0.15

(c) 0.05

(d) 0.005

Answer: (c)

Explanation :

14c

Q35. 35  is equal to ::

(a) 0.0002

(b) 0.002

(b) 0.02

(d) 0.2

Answer: (d)

Explanation :

15b

Q36. The sum of the cubes of the numbers 22, - 15 and – 7 is equal to

(a) 6930

(b) 9630

(c) 3

(d) 0

Answer: (a)

Explanation :

16a

Q37. If the square root of x is the cube root of y, then the relation between x and y is

(a) x3 = y2

(b) x2 = y3

(c) x = y

(d) x6 = y5

Answer: (a)

Explanation :

17a

Q38. (5.5)3 – (4.5)3 is equal to:

(a) 1

(b) 75

(c) 74.25

(d) 75.25

Answer: (d)

Explanation :

18d

Q39. The sum of the digits of the smallest number which, when multiplied by 1800, gives a perfect cube, is:

(a) 2

(b) 3

(c) 6

(d) 8

Answer: (c)

Explanation :

19c

Q40. Which of the following is a perfect square as well as a cube? 343, 125, 81, or 64

(a) 81

(b) 125

(c) 343

(d) 64

Answer: (d)

Explanation :

343 = 7 ×7×7   ;

125 = 5× 5×5   ;

81 = 3×3×3×3 ;

64 = 8 ×8=4×4×4

We see that 343 and 125 are only perfect cubes of 7 and 5 respectively. 81 is only is perfect square of 9. 64 is a perfect square of 8 as well as a perfect cube of 4.