# Square and Cube Roots Quiz Set 017

### Question 1

What is √(4320) × √(4320)?

A

4320.

B

4400.

C

4416.

D

4520.

Soln.
Ans: a

We can see that √(4320) × √(4320) is same as √(2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 ) × √(2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 ) which equals √(210 × 36 × 52), which equals (25 × 33 × 51), which gives 4320.

### Question 2

If \$√2\$ = 1.41, then what is the value of \${√2}/5\$ − \$13/{√2}\$ + \$√8\$?

A

-6.081.

B

+6.081.

C

-6.009.

D

+6.009.

Soln.
Ans: a

The given expression can be simplified to \${{(√2)^2} - {5 × 13} + {5 × √2 × √{2 × 2^2}}}/{5 × √2}\$, which is same as \${2 - 65 + 20}/{5 × √2}\$, which is same as \${-43/{5 × √2}\$. Rationalizing, we get \${-43/{5 × √2} × {√2/√2}\$ which gives \${-43√2}/10\$ which = -6.081.

### Question 3

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 4

What is √0.0036?

A

0.06.

B

0.36.

C

0.12.

D

0.09.

Soln.
Ans: a

We can see that 0.06 × 0.06 = 0.0036, so square root is 0.06.

### 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.