# Square and Cube Roots Quiz Set 002

### Question 1

What is the value of \${√7}/6\$ − \$3/{√7}\$?

A

\${-11√7}/42\$.

B

\${+11√7}/42\$.

C

\${-13√7}/42\$.

D

\${+13√7}/42\$.

Soln.
Ans: a

The given expression can be simplified to \${{(√7)^2} - 6 × 3}/{6 × √7}\$, which is same as \${7 - 18}/{6 × √7}\$, which is same as \${-11/{6 × √7}\$. Rationalizing, we get \${-11/{6 × √7} × {√7/√7}\$ which gives \${-11√7}/42\$

### Question 2

What is the least number that should be subtracted from 0.0604 to make it a perfect square?

A

0.06.

B

0.05.

C

0.04.

D

0.02.

Soln.
Ans: a

We know that 0.02 = \$√0.0004\$, so by inspection we can see that 0.0604 - 0.06 will give us 0.0004.

### Question 3

If \$√2\$ = 1.41, then what is the value of \${√2}/5\$ − \$11/{√2}\$?

A

-7.495.

B

+7.495.

C

-9.81.

D

+9.81.

Soln.
Ans: a

The given expression can be simplified to \${{(√2)^2} - 5 × 11}/{5 × √2}\$, which is same as \${2 - 55}/{5 × √2}\$, which is same as \${-53/{5 × √2}\$. Rationalizing, we get \${-53/{5 × √2} × {√2/√2}\$ which gives \${-53√2}/10\$ which = -7.495.

### Question 4

Each car of a garage has as many litres of petrol as is the total number of cars in that garage. If there are 196 litres of petrol in all, how many cars are there?

A

14.

B

12.

C

7.

D

8.

Soln.
Ans: a

Let the number of cars = n. So litres of petrol in one car are also n, and therefore, litres of petrol in n cars = \$n^2\$. We have been given \$n^2 = 196\$, which gives n = 14.

### Question 5

One-fourth of the cube-root of which number is 0.7?

A

21.952.

B

49.

C

64.235.

D

49.64.

Soln.
Ans: a

Let the number be n. So \${1/4} × √^3n\$ = 0.7, which gives \$√^3n\$ = 4 × 0.7 = 2.8. so n = \$2.8^3\$ = 21.952. 