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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 ‘8’ 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) n² + 1

(d) (2n² – 1) / 2

## Solution:

(b) n(n + 1) / 2

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

5. √625 = ?

(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.

√625 = √25 X 25 = 25.

Option (c) is the answer.

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. √0.81 = ?

(a) 0.9

(b) 0.09

(c) 0.99

(d) 0.96

## Solution:

(a) 0.9

√0.81 =√0.9 X 0.9 = 0.9.

Option (a) is the answer.

8. √0.00065536 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.

Option (b) is the answer.

9. √1.0219 = ?

(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.

Option (a) is the answer.

10. √0.25 × √1.6 = ?

(a) 0.15

(b) 0.2

(c) 0.25

(d) 20

## Solution:

(b) 0.2

√0.25 × √1.6 =√0.5 x 0.5× √0.4 x 0.4

= 0.5 x 0.4 = 0.2.

Option (b) is the answer.

11. √289/√256 = ?

(a) 3 / 25

(b) 30 √32

(c) 17 / 16

(d) 1.25

## Solution:

(c) 17 / 16

√289/√256 = √17 X 17 / √16 X 16.

= 17 / 16.

Option (c) is the answer.

12. √6084/144 = ?

(a) 22 / 17

(b) 25 / 12

(c) 32 / 4

(d) 39 / 6

## Solution:

(d) 39 / 6

√6084/144 =√ 78 X 78 / 12 X 12.

= 78 / 12.

= 2 x 39 / 2 x 6.

= 39 / 6.

Option (d) is the answer.

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 √4562496

(a) 2256

(b) 2136

(c) 2563

(d) 2222

## Solution:

(b) 2136

√4562496 = √2136 X 2136.

= 2136.

Option (b) is the answer.

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.

Option (b) is the answer.

16. 15^2 + √0.81 + 25 = ?

(a) 250.9

(b) 252.9

(c) 251.9

(d) 255.9

## Solution:

(a) 250.9

15^2 + √0.81 + 25 = 15 X 15 + √0.9 X 0.9 + 25.

= 225 + 0.9 + 25.

= 250.9.

Option (a) is the answer.

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 – 31.25 = 218.75.

option (d) is answer.

18.√ 324 + √576 = ?

(a) 42

(b) 52

(c) 62

(d) 72

## Solution:

(a) 42

√ 324 + √576 = √ 18 X 18 + √24 X 24.

= 18 + 24.

= 42.

Option (a) is the answer.

19.√ 625/ 25 + √ 289 / 17 + √ 256 / 4 = ?

(a) 2

(b) 3

(c) 4

(d) 5

## Solution:

(d) 5

√ 625/ 25 + √ 289 / 17 + √ 256 / 4 =√ 25 x 25 / 25 + √ 17 x 17 / 17 + √ 16 x 16 / 4.

= 25 / 25 + 17 / 17 + 16 / 4.

= 1 + 1 + 4.

= 5.

Option (d) is the answer.

20. √25 x √49 x √36 = ?

(a) 250

(b) 210

(c) 240

(d) 260

## Solution:

(b) 210

√25 x √49 x √36 = √5 x 5 x √7 x 7 x √6 x 6 = 5 x 7 x 6 = 210.

Option (b) is the answer.