# Practice Test on Square and Square Roots | Multiple Choice Questions on Square and Square Roots

In practice tests on square and square roots, we are providing different methods of problems with solutions. We are providing four options for every question. Practice the test paper on square roots and find the correct answer for the given questions. Improve your preparation level for every problem. Different methods included for every problem. Therefore, choose the best and easy method and learn the problems.

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## Objective Questions on Square and Square Roots

1 . Which of the following numbers is a perfect square?
(a) 131
(b) 144
(c) 165
(d) 251

Solution:

(b) 144

We need to find the perfect square number from the above options.
11 X 11 = 121
12 X 12 = 144
13 X 13 = 169
14 X 14 = 196
15 X 15 = 225
16 X 16 = 256
Frm the given numbers, there is only option available that is a perfect square.
So, the perfect square number is 144. So the answer is an option (b).

2. A perfect square number can never have the digit …… at the unit’s place.
(a) 6
(b) 4
(c) 8
(d) 5

Solution:

(c) 8

Firstly, we need to identify the unit’s place of the perfect square number.
1 X 1 = 1
2 X 2 = 4
3 X 3 = 9
4 X 4 = 16
5 X 5 = 25
6 X 6 = 36
7 X 7 = 49
8 X 8 = 64
9 X 9 = 81
10 X 10 = 100
In the units place we will get the numbers like 1, 4, 9, 6, 5, and 0.
So, the square numbers can never have the digit â€˜8â€™ at the unit’s place.

3. Which of the following is a Pythagorean triplet?
(a) (2, 4, 6)
(b) (5, 8, 2)
(c) (2, 9, 5)
(d) (3, 4, 5)

Solution:

(d) (3, 4, 5)

Pythagorean triplet isX^2 + Y^2 = Z^2
(a) (2, 4, 6)
Here, x = 2, y = 4, z = 6.
2^2 + 4^2 = 6^2.
4 + 16 = 36.
20 is not equal to 36.
(b) (5, 8, 2)
Here, x = 5, y = 8, z = 2.
5^2 + 8^2 = 2^2.
25 + 64 = 4.
91 is not equal to 4.
(c) (2, 9, 5)
Here, x = 2, y = 9, z = 5.
2^2 + 9^2 = 5^2.
4 + 81 = 25.
85 is not equal to 25.
(d) (3, 4, 5)
Here, x = 3, y = 4, z = 5.
3^2 + 4^2 = 5^2.
9 + 16 = 25.
25 is equal to 25.
So, (3, 4, 5) is a Pythagorean triplet.
Option (d) is Pythagorean triplet.

4. Sum of the first n natural numbers is
(a) n^2
(b) n(n + 1) / 2
(c) nÂ² + 1
(d) (2nÂ² – 1) / 2

Solution:

(b) n(n + 1) / 2

Sum of the first n natural numbers is n(n + 1) / 2.

5. âˆš625 = ?
(a) 45
(b) 35
(c) 25
(d) 55

Solution:

(c) 25

45 X 45 = 2025.
35 X 35 = 1225.
25 X 25 = 625.
55 X 55 = 3025.
âˆš625 = âˆš25 X 25 = 25.

6. What least number must be added to 720 to make it a perfect square?
(a) 5
(b) 2
(c) 7
(d) 9

Solution:

(d) 9

720 + 5 = 725.
720 + 2 = 722.
720 + 7 = 727.
720 + 9 = 729.
27 X 27 = 729.

9 should be added to 720 to make it a perfect square number.

7. âˆš0.81 = ?
(a) 0.9
(b) 0.09
(c) 0.99
(d) 0.96

Solution:

(a) 0.9

âˆš0.81 =âˆš0.9 X 0.9 = 0.9.

8. âˆš0.00065536 is equal to
(a) 0.256
(b) 0.0256
(c) 0.00256
(d) 0.000256

Solution:

(b) 0.0256

(a) 0.256 X 0.256 = 0.065536.
(b) 0.0256 X 0.0256 = 0.00065536.
(c) 0.00256 X 0.00256 = 0.0000065536.
(d) 0.000256 X 0.000256 = 6.5536e-8.

9. âˆš1.0219 = ?
(a) 1.0109
(b) 1.03
(c) 0.505
(d) 1.056

Solution:

(a) 1.0109

(a) 1. 0109 X 1.0109 = 1.0219.
(b) 1. 03 X 1.03 = 1.0609.
(c) 0.505 X 0.505 = 0.255025.
(d) 1. 056 X 1.056 = 1.115136.

10. âˆš0.25 Ã— âˆš1.6 = ?
(a) 0.15
(b) 0.2
(c) 0.25
(d) 20

Solution:

(b) 0.2

âˆš0.25 Ã— âˆš1.6 =âˆš0.5 x 0.5Ã— âˆš0.4 x 0.4
= 0.5 x 0.4 = 0.2.

11. âˆš289/âˆš256 = ?
(a) 3 / 25
(b) 30 âˆš32
(c) 17 / 16
(d) 1.25

Solution:

(c) 17 / 16

âˆš289/âˆš256 = âˆš17 X 17 / âˆš16 X 16.
= 17 / 16.

12. âˆš6084/144 = ?
(a) 22 / 17
(b) 25 / 12
(c) 32 / 4
(d) 39 / 6

Solution:

(d) 39 / 6

âˆš6084/144 =âˆš 78 X 78 / 12 X 12.
= 78 / 12.
= 2 x 39 / 2 x 6.
= 39 / 6.

13. Find the square root of 3844
(a) 56
(b) 52
(c) 62
(d) 65

Solution:

(c) 62

Square root of 3844 = 62 X 62.
So, the square root of 3844 is 62
Option ( c) is the answer.

14. Evaluate âˆš4562496
(a) 2256
(b) 2136
(c) 2563
(d) 2222

Solution:

(b) 2136

âˆš4562496 = âˆš2136 X 2136.
= 2136.

15. Find the value of 49^2 X 25^2 = ?
(a) 1501621
(b) 1500625
(c ) 1502624
(d)1500725

Solution:

(b) 1500625

49^2 X 25^2 = (49 X 49) X (25 X 25).
= 2401 X 625.
= 1500625.

16. 15^2 + âˆš0.81 + 25 = ?
(a) 250.9
(b) 252.9
(c) 251.9
(d) 255.9

Solution:

(a) 250.9

15^2 + âˆš0.81 + 25 = 15 X 15 + âˆš0.9 X 0.9 + 25.
= 225 + 0.9 + 25.
= 250.9.

17. 25% of 125 + ? = 250
(a) 218
(b) 220.75
(c) 225.75
(d) 218.75

Solution:

(d) 218.75

25% of 125 + x = 250.
25 / 100 (125) + x = 250.
31.25 + x = 250.
x = 250 â€“ 31.25 = 218.75.

18.âˆš 324 + âˆš576 = ?
(a) 42
(b) 52
(c) 62
(d) 72

Solution:

(a) 42

âˆš 324 + âˆš576 = âˆš 18 X 18 + âˆš24 X 24.
= 18 + 24.
= 42.

19.âˆš 625/ 25 + âˆš 289 / 17 + âˆš 256 / 4 = ?
(a) 2
(b) 3
(c) 4
(d) 5

Solution:

(d) 5

âˆš 625/ 25 + âˆš 289 / 17 + âˆš 256 / 4 =âˆš 25 x 25 / 25 + âˆš 17 x 17 / 17 + âˆš 16 x 16 / 4.
= 25 / 25 + 17 / 17 + 16 / 4.
= 1 + 1 + 4.
= 5.

20. âˆš25 x âˆš49 x âˆš36 = ?
(a) 250
(b) 210
(c) 240
(d) 260

Solution:

(b) 210

âˆš25 x âˆš49 x âˆš36 = âˆš5 x 5 x âˆš7 x 7 x âˆš6 x 6 = 5 x 7 x 6 = 210.