# Square and Cube Roots Quiz Set 016

### Question 1

What is cube root of 0.000512?

A

0.08.

B

0.16.

C

0.016.

D

1.6.

Soln.
Ans: a

We can see that 0.08 × 0.08 × 0.08 = 0.000512, so cube root is 0.08.

### Question 2

What is the least number that should be subtracted from 0.0449 to make it a perfect square?

A

0.04.

B

0.06.

C

0.05.

D

0.004.

Soln.
Ans: a

We know that 0.07 = \$√0.0049\$, so by inspection we can see that 0.0449 - 0.04 will give us 0.0049.

### Question 3

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 4

What is the value of \$√{(13 - 3√5) × (13 + 3√5)}\$?

A

\$√124\$.

B

\$√248\$.

C

\$√196\$.

D

\$√416\$.

Soln.
Ans: a

By inspection, we can easily see that the formula (a - b) × (a + b) can be used to simplify like this: \$√{(13)^2 - (3√5)^2}\$, which is same as \$√{169 - (3^2 × 5)}\$, which is same as \$√{169 - 45}\$ = \$√124\$.

### Question 5

If x = 0.2054, then what is the value of \$8x + √{16x^2 - 8x + 1}\$?

A

1.82.

B

1.414.

C

2.236.

D

1.732.

Soln.
Ans: a

By inspection, \$8x + √{16x^2 - 8x + 1}\$ is same as \$8x + √{({1 - 4x})^2}\$, which is same as 8x + (1 - 4x) = 1 + 4x = 1.82. This Blog Post/Article "Square and Cube Roots Quiz Set 016" 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