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Class 8

Explore popular questions from Squares and Square Roots for Class 8. This collection covers Squares and Square Roots previous year Class 8 questions hand picked by experienced teachers.

Squares and Square Roots

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Q 1. The smallest number by which 136 must be multiplied so that it becomes a perfect square is

A

2

B

17

34

D

None of these

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Q 2. The product of the two numbers is 1936. If one number is 4 times the other, the numbers are

A

16, 121

22, 88

C

44, 44

D

None of these

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Q 3. The least square number exactly divisible by 4, 6, 10, 15 is

A

400

B

100

C

25

900

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Q 4. The value of {tex}\sqrt{388+\sqrt{127+\sqrt{289}}}{/tex} is

A

17

B

12

20

D

None of these

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Q 5. A gardener arranges plants in rows to form a square. He finds that in doing so 15 plants are left out. If the total number of plants is 3984, the number of plants in each row is

A

62

63

C

64

D

None of these

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Q 6. If a is a natural number then {tex}a^2+\frac{1}{a^2}{/tex} is always greater than or equal to

A

6

B

4

C

3

2

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Q 7. If {tex}\sqrt{0.04\times 0.4\times a}=0.4\times 0.04\times \sqrt{b}{/tex}, then value of {tex}\frac{b}{a}{/tex}

A

0.016

{tex}\frac{125}{2}{/tex}

C

0.16

D

None of these

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Q 8. The hypotenuse of an isosceles right-angled triangular field has a length of {tex}30\sqrt{2}{/tex} m, then the length of other side is

A

{tex}30\sqrt{2}{/tex}

30 m

C

25 m

D

None of these

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Q 9. The sides of a triangle are denoted by x, y and z. Area of the triangle and semi perimeter of the triangle are denoted by P and q respectively. If P = {tex}\sqrt{q(q-x)(q-y)(q-z)}{/tex} and {tex}x+y-z=y+z-x=z+x-y=4{/tex}. Find P (in square units).

A

{tex}2\sqrt{3}{/tex}

B

{tex}3\sqrt{3}{/tex}

{tex}4\sqrt{3}{/tex}

D

{tex}6\sqrt{3}{/tex}

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Q 10. Find the square root of {tex}\frac{81b^2a^4}{36x^2y^6}{/tex}

{tex}\frac{3ba^2}{2xy^3}{/tex}

B

{tex}\frac{3b^2a}{2x^2y}{/tex}

C

{tex}\frac{3ba}{2x^3y}{/tex}

D

{tex}\frac{3ba}{2xy^2}{/tex}

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Q 11. Which of the following can be a perfect square?

A

A number ending in 3 or 7

B

A number ending with odd number of zeros

A number ending with even number of zeros

D

A number ending in 2.

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Q 12. Which of the following can be the square of a natural number 'n'?

A

sum of the squares of first n natural numbers

B

sum of the first n natural numbers

C

sum of first (n - 1) natural numbers

sum of first 'n' odd natural numbers

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Q 13. Which of the following is the number of non-perfect square numbers between the squares of the numbers n and n + 1?

A

n + 1

B

n

2n

D

2n + 1

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Q 14. Which of the following is the difference between the squares of two consecutive natural numbers is

sum of the two numbers

B

difference of the numbers

C

twice the sum of the two numbers

D

twice the sum of the two numbers

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Q 15. Which of the following is the number of a non-perfect square numbers between 17{tex}^2{/tex} and 18{tex}^2{/tex}?

A

613

B

35

34

D

70

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Q 16. Which of the following is the number of zeros in the square of 900?

A

3

4

C

5

D

2

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Q 17. If a number of n-digits is a perfect square and 'n' is an even number, then which of the following is the number of digits of its square root?

A

{tex}\frac{n-1}{2}{/tex}

{tex}\frac{n}{2}{/tex}

C

{tex}\frac{n+1}{2}{/tex}

D

{tex}2n{/tex}

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Q 18. If a number of n-digit is a perfect square and 'n' is an odd number then which of the following is the number of digits of its square root?

A

{tex}\frac{n-1}{2}{/tex}

B

{tex}\frac{n}{2}{/tex}

{tex}\frac{n+1}{2}{/tex}

D

{tex}2n{/tex}

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Q 19. Which of the following is a Pythagorean-triplet?

A

{tex}n, (n^2- 1){/tex} and {tex}(n^2 + 1){/tex}

B

{tex}(n-1), (n^2- 1){/tex} and {tex}(n^2 + 1){/tex}

C

{tex}(n + 1), (n^2- 1){/tex} and {tex}(n^2 + 1){/tex}

{tex}2n, (n^2- 1){/tex} and {tex}(n^2 + 1){/tex}

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Q 20. The greatest perfect square of a natural number smaller than {tex}(51)^2{/tex} is

A

50

2500

C

3600

D

2551

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Q 21. {tex}\sqrt{176+\sqrt{2401}}{/tex} is equal to

A

12

B

13

C

14

15

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Q 22. If {tex}\frac{1872}{\sqrt{x}}=234{/tex}, then x is equal to

A

8

64

C

256

D

4

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Q 23. If 140{tex}\sqrt{x}{/tex}+315=1015 , then x is equal to

A

15

B

225

C

5

25

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Q 24. The greatest four digit number which is also a perfect square is

A

9701

9801

C

9901

D

None of these