# Square and Cube Roots Quiz Set 010

### Question 1

One-fourth of the square-root of which number is 0.6?

A

5.76.

B

.5.24

C

5.96.

D

5.49.

Soln.
Ans: a

Let the number be n. So \${1/4} × √n\$ = 0.6, which gives \$√n\$ = 4 × 0.6 = 2.4. so n = \$2.4^2\$ = 5.76.

### Question 2

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 3

What is the value of \$(√5 - 1/√5)^2\$?

A

\$3{1/5}\$.

B

\$3{2/5}\$.

C

\$3{3/5}\$.

D

\$3{4/5}\$.

Soln.
Ans: a

I will give a general solution for any n. \$(√n - 1/√n)^2\$ is same as \$({(√n)^2 - 1}/√n)^2\$ which becomes \$(n - 1)^2/n\$. Putting n = 5, we get \${16/5}\$, which is same as: \$3{1/5}\$.

### Question 4

What is the value of \$√{(11 - 2√3) × (11 + 2√3)}\$?

A

\$√109\$.

B

9.

C

10.

D

√3.

Soln.
Ans: a

By inspection, we can easily see that the formula (a - b) × (a + b) can be used to simplify like this: \$√{(11)^2 - (2√3)^2}\$, which is same as \$√{121 - (2^2 × 3)}\$, which is same as \$√{121 - 12}\$ = \$√109\$.

### Question 5

One-fourth of the cube-root of which number is 0.4?

A

4.096.

B

4.024.

C

4.256.

D

4.128.

Soln.
Ans: a

Let the number be n. So \${1/4} × √^3n\$ = 0.4, which gives \$√^3n\$ = 4 × 0.4 = 1.6. so n = \$1.6^3\$ = 4.096.