# Square and Cube Roots Quiz Set 013

### Question 1

If \$√5\$ = 2.24, then what is the value of \${√5}/2\$ − \$4/{√5}\$?

A

-0.671.

B

+0.671.

C

6.71.

D

-6.71.

Soln.
Ans: a

The given expression can be simplified to \${{(√5)^2} - 2 × 4}/{2 × √5}\$, which is same as \${5 - 8}/{2 × √5}\$, which is same as \${-3/{2 × √5}\$. Rationalizing, we get \${-3/{2 × √5} × {√5/√5}\$ which gives \${-3√5}/10\$ which = -0.671.

### Question 2

What is the value of \${√16/6}\$ × \${5/√4}\$ × \${6/√25}\$?

A

2.

B

3.

C

1.

D

4.

Soln.
Ans: a

The given expression can be simplified to \${√2^4/6}\$ × \${5/√2^2}\$ × \${6/√5^2}\$, which is same as \${2^2/6}\$ × \${5/2}\$ × \${6/5}\$, which cancels to 2.

### Question 3

One-fifth of the cube-root of which number is 0.3?

A

3.375.

B

3.250.

C

3.125.

D

3.325.

Soln.
Ans: a

Let the number be n. So \${1/5} × √^3n\$ = 0.3, which gives \$√^3n\$ = 5 × 0.3 = 1.5. so n = \$1.5^3\$ = 3.375.

### Question 4

What is the value of \${√5}/3\$ − \$2/{√5}\$?

A

\${-1√5}/15\$.

B

\${+1√5}/15\$.

C

\${-2√5}/15\$.

D

\${+2√5}/15\$.

Soln.
Ans: a

The given expression can be simplified to \${{(√5)^2} - 3 × 2}/{3 × √5}\$, which is same as \${5 - 6}/{3 × √5}\$, which is same as \${-1/{3 × √5}\$. Rationalizing, we get \${-1/{3 × √5} × {√5/√5}\$ which gives \${-1√5}/15\$

### Question 5

If x = 0.7342, then what is the value of \$11x + √{16x^2 - 8x + 1}\$?

A

6.14.

B

12.28.

C

3.14.

D

3.07.

Soln.
Ans: a

By inspection, \$11x + √{16x^2 - 8x + 1}\$ is same as \$11x + √{({1 - 4x})^2}\$, which is same as 11x + (1 - 4x) = 1 + 7x = 6.14. This Blog Post/Article "Square and Cube Roots Quiz Set 013" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-04-20