Square roots and Cube Roots is an important topic in the Quantitative section of the Aptitude exam. Questions in this section are framed in a confusing way. So, make sure that you practice different level of questions in order to have flexibility while solving problems related to this concept.

Important topics covered in this section are the basics of Squares and square roots, basic questions, find unknown value, etc. To make your preparation easy we have compiled the most important 20 questions from this topic. Make sure you dedicate considerable time to solve these questions with integrity.

We assume that you have completed Simplification practice before coming to this page if not make sure you solve questions from Simplifications first. Second, after you complete this section solve questions from Averages.

If you are already thorough with all the concepts of quantitative aptitude then move on to reasoning ability and verbal ability.

Q1

Solve (\(\frac{\sqrt{25}}{\sqrt{9}}\)-\(\frac{\sqrt{64}}{\sqrt{81}}\))**÷**\(\frac{\sqrt{16}}{\sqrt{324}}\)=?

Level 1
Squares and Square Roots
Basic Questions

A

4.5

B

2.5

C

1.5

D

3.5

Q2

The square root of \((7+3\sqrt{5})(7-3\sqrt{5})\) is:

Level 1
Squares and Square Roots
Basic Questions

A

\(\sqrt{5}\)

B

2

C

4

D

\(3\sqrt{5}\)

Q3

\(\left ( \sqrt{3}-\frac{1}{\sqrt{3}} \right )^{2}\) Simplifies to:

Level 1
Squares and Square Roots
Basic Questions

A

\(\frac{3}{4}\)

B

\(\frac{4}{\sqrt{3}}\)

C

\(\frac{4}{3}\)

D

none of these

Q4

\(\sqrt{1.5625}\)=?

Level 1
Squares and Square Roots
Find Unknown Value
Basic Questions

A

1.05

B

1.25

C

1.45

D

1.55

Q5

Evaluate: \(\sqrt{41-\sqrt{21+\sqrt{19-\sqrt{9}}}}\)

Level 1
Squares and Square Roots
Simplification of Square Roots

A

3

B

5

C

6

D

6.4

Q6

If 0.13 ÷ p² = 13, then p equals:

Level 1
Squares and Square Roots
Find Unknown Value
Simplification of Square Roots

A

0.01

B

0.1

C

10

D

100

Q7

If \(\sqrt{4096}\)=64, then the value of \(\sqrt{40.96}\)+\(\sqrt{0.4096}\)+\(\sqrt{0.004096}\)+\(\sqrt{0.00004096}\) up to two places of decimals is

Level 1
Squares and Square Roots
Simplification of Square Roots

A

7.09

B

7.10

C

7.11

D

7.12

Q8

What is \(\frac{5+\sqrt{10}}{5\sqrt{5}-2\sqrt{20}-\sqrt{32}+\sqrt{50}}\)=?

Level 1
Squares and Square Roots
Simplification of Square Roots

A

5

B

5\(\sqrt{2}\)

C

5\(\sqrt{5}\)

D

\(\sqrt{5}\)

Q9

The approximate value of \(\frac{3\sqrt{12}}{2\sqrt{28}}\div\frac{2\sqrt{21}}{\sqrt{98}}\) is:

Level 2
Squares and Square Roots
Simplification of Square Roots

A

1.0605

B

1.0727

C

1.6007

D

1.6026

Q10

\(\left [ \frac{3\sqrt{2}}{\sqrt{6}-\sqrt{3}}-\frac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}} -\frac{6}{\sqrt{8}-\sqrt{12}}\right ]=?\)

Level 2
Squares and Square Roots
Simplification of Square Roots

A

\(\sqrt{3}-\sqrt{2}\)

B

\(\sqrt{3}+\sqrt{2}\)

C

\(5\sqrt{3}\)

D

1

Q11

The least perfect square, which is divisible by each of 21, 36 and 66, is:

Level 2
Squares and Square Roots
Perfect Squares

A

213444

B

214344

C

214434

D

231444

Q12

What is the least number which should be subtracted from 0.000326 to make it a perfect square?

Level 2
Squares and Square Roots
Perfect Squares

A

0.000002

B

0.000004

C

0.02

D

0.04

Q13

How many two-digit numbers satisfy this property: the last digit (unit's digit) of the square of the two-digit number is 8?

Level 2
Squares and Square Roots
Perfect Squares

A

1

B

2

C

3

D

none of these

Q14

If \(\sqrt{x+\frac{x}{y}}\) = x\(\sqrt{\frac{x}{y}}\) , where x and y are positive real numbers, then y is equal to

Level 2
Squares and Square Roots
Find Unknown Value

A

x+1

B

x-1

C

\(x^{2}\)+1

D

\(x^{2}\)-1

Q15

A man bought some eggs of which 10% are rotten. He gives 80% of the remainder to his neighbors. Now he is left out with 36 eggs. How many eggs he bought?

Level 2
Problems on Numbers
Find Unknown Value

A

40

B

100

C

200

D

72

Q16

While solving a mathematical problem, Samidha squared a number and then subtracted 25 from it rather than the required i.e., first subtracting 25 from the number and then squaring it. But she got the right answer. What was the given number?

Level 2
Squares and Square Roots
Find Unknown Value

A

13

B

38

C

48

D

Cannot be determined

E

none of these

Q17

\(\frac{\sqrt{3+x}+\sqrt{3-x}}{\sqrt{3+x}-\sqrt{3-x}}\)=2. Then x is?

Level 3
Squares and Square Roots
Other Type Questions

A

\(\frac{5}{7}\)

B

\(\frac{7}{5}\)

C

\(\frac{5}{12}\)

D

\(\frac{12}{5}\)

Q18

If x = \(\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\) and y= \(\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}\) then x+y is

Level 3
Squares and Square Roots
Other Type Questions

A

2\(\sqrt{5}+\sqrt{3}\)

B

2\(\sqrt{15}\)

C

8

D

16

Q19

A mobile company offered to pay the Indian Cricket Team as much money per run scored by the side as the total number it gets in a one-dayer against Australia. Which one of the following cannot be the total amount to be spent by the company in this deal.

Level 3
Squares and Square Roots
Perfect Squares

A

21,904

B

56,169

C

1,01,761

D

1,21,108

Q20

If the product of four consecutive natural numbers increased by a natural number p, is a perfect square, then the value of p is

Level 3
Squares and Square Roots
Find Unknown Value

A

1

B

2

C

4

D

8

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20