Square and Cube Roots Quiz Set 001

Question 1

One-third of the cube-root of which number is 0.6?

A

5.832.

B

5.200.

C

5.414.

D

5.173.

Soln.
Ans: a

Let the number be n. So \${1/3} × √^3n\$ = 0.6, which gives \$√^3n\$ = 3 × 0.6 = 1.8. so n = \$1.8^3\$ = 5.832.

Question 2

What is cube root of 0.000008?

A

0.02.

B

0.002.

C

0.2.

D

0.0002.

Soln.
Ans: a

We can see that 0.02 × 0.02 × 0.02 = 0.000008, so cube root is 0.02.

Question 3

If \$2√3 + √27 = 8.66\$, then what is the value of \$√27 + 4√3\$?

A

12.12.

B

12.24.

C

12.00.

D

12.36.

Soln.
Ans: a

The given expression can be rearranged like this: \$2√3 + √{3^{2} × 3}\$, which is same as \$2√3 + 3√3\$ which is same as \$5√3 = 8.66\$, from which we get \$√3 = 1.73\$. Next we can see that \$√27 + 4√3\$ is same as \$√{3^{2} × 3} + 4√3\$, which is same as \$7√3\$, which gives \$7 × 1.73\$ = 12.12.

Question 4

What is the value of \${√17}/6\$ − \$5/{√17}\$?

A

\${-13√17}/102\$.

B

\${+13√17}/102\$.

C

\${-5√17}/102\$.

D

\${+5√17}/102\$.

Soln.
Ans: a

The given expression can be simplified to \${{(√17)^2} - 6 × 5}/{6 × √17}\$, which is same as \${17 - 30}/{6 × √17}\$, which is same as \${-13/{6 × √17}\$. Rationalizing, we get \${-13/{6 × √17} × {√17/√17}\$ which gives \${-13√17}/102\$

Question 5

If \$4√5 + √80 = 17.89\$, then what is the value of \$√125 + 6√5\$?

A

24.60.

B

12.25.

C

25.

D

12.96.

Soln.
Ans: a

The given expression can be rearranged like this: \$4√5 + √{4^{2} × 5}\$, which is same as \$4√5 + 4√5\$ which is same as \$8√5 = 17.89\$, from which we get \$√5 = 2.24\$. Next we can see that \$√125 + 6√5\$ is same as \$√{5^{2} × 5} + 6√5\$, which is same as \$11√5\$, which gives \$11 × 2.24\$ = 24.60. This Blog Post/Article "Square and Cube Roots Quiz Set 001" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.