# Square and Cube Roots Quiz Set 011

### Question 1

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

A

0.216.

B

0.256.

C

0.128.

D

0.144.

Soln.
Ans: a

Let the number be n. So \${1/2} × √^3n\$ = 0.3, which gives \$√^3n\$ = 2 × 0.3 = 0.6. so n = \$0.6^3\$ = 0.216.

### Question 2

If \$√5\$ = 2.24, then what is the value of \${√5}/2\$ − \$2/{√5}\$ + \$√125\$?

A

11.404.

B

1.414.

C

22.414.

D

0.707

Soln.
Ans: a

The given expression can be simplified to \${{(√5)^2} - {2 × 2} + {2 × √5 × √{5 × 5^2}}}/{2 × √5}\$, which is same as \${5 - 4 + 50}/{2 × √5}\$, which is same as \${51/{2 × √5}\$. Rationalizing, we get \${51/{2 × √5} × {√5/√5}\$ which gives \${51√5}/10\$ which = 11.404.

### Question 3

If \$√2\$ = 1.41, then what is the value of \${√2}/5\$ − \$2/{√2}\$ + \$√8\$?

A

1.697.

B

1.414.

C

1.732.

D

0.707.

Soln.
Ans: a

The given expression can be simplified to \${{(√2)^2} - {5 × 2} + {5 × √2 × √{2 × 2^2}}}/{5 × √2}\$, which is same as \${2 - 10 + 20}/{5 × √2}\$, which is same as \${12/{5 × √2}\$. Rationalizing, we get \${12/{5 × √2} × {√2/√2}\$ which gives \${12√2}/10\$ which = 1.697.

### Question 4

If x = 0.8547, then what is the value of \$4x + √{16x^2 - 8x + 1}\$?

A

1.

B

16.

C

2.

D

4.

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.

### Question 5

What is √0.0004?

A

0.02.

B

0.4.

C

0.2.

D

0.002.

Soln.
Ans: a

We can see that 0.02 × 0.02 = 0.0004, so square root is 0.02.