# Square and Cube Roots Quiz Set 017

### Question 1

What is the value of \${√17}/3\$ − \$2/{√17}\$?

A

\${11√17}/51\$.

B

\${-11√17}/51\$.

C

\${9√17}/51\$.

D

\${-9√17}/51\$.

Soln.
Ans: a

The given expression can be simplified to \${{(√17)^2} - 3 × 2}/{3 × √17}\$, which is same as \${17 - 6}/{3 × √17}\$, which is same as \${11/{3 × √17}\$. Rationalizing, we get \${11/{3 × √17} × {√17/√17}\$ which gives \${11√17}/51\$

### Question 2

What is the value of \$√{3 + √36}\$?

A

3.

B

9.

C

4.

D

6.

Soln.
Ans: a

The given expression is same as \$√{3 + √6^2}\$, which becomes \$√{3 + 6}\$, or \$√9\$ which gives 3 as the answer. Please note that squares of as many numbers should be always on your tips.

### Question 3

Each canvas of a group of canvases has as many dots as is the total number of canvases in that group of canvases. If there are 144 dots in all, how many canvases are there?

A

12.

B

14.

C

22.

D

16.

Soln.
Ans: a

Let the number of canvases = n. So dots in one canvas are also n, and therefore, dots in n canvases = \$n^2\$. We have been given \$n^2 = 144\$, which gives n = 12.

### Question 4

One-third of the square-root of which number is 0.3?

A

0.81.

B

0.9.

C

0.09.

D

0.3.

Soln.
Ans: a

Let the number be n. So \${1/3} × √n\$ = 0.3, which gives \$√n\$ = 3 × 0.3 = 0.9. so n = \$0.9^2\$ = 0.81.

### Question 5

If x = 0.7727, then what is the value of \$4x + √{16x^2 - 8x + 1}\$?

A

1.

B

8.

C

16.

D

9.

Soln.
Ans: a

By inspection, \$4x + √{16x^2 - 8x + 1}\$ is same as \$4x + √{({1 - 4x})^2}\$, which is same as 4x + (1 - 4x) = 1. 