# Square and Cube Roots Quiz Set 011

### Question 1

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 2

One-fourth of the square-root of which number is 0.9?

A

12.96.

B

12.56.

C

9.25.

D

9.50.

Soln.
Ans: a

Let the number be n. So \${1/4} × √n\$ = 0.9, which gives \$√n\$ = 4 × 0.9 = 3.6. so n = \$3.6^2\$ = 12.96.

### Question 3

Each book of a shelf has as many pages as is the total number of books in that shelf. If there are 169 pages in all, how many books are there?

A

13.

B

16.

C

24.

D

9.

Soln.
Ans: a

Let the number of books = n. So pages in one book are also n, and therefore, pages in n books = \$n^2\$. We have been given \$n^2 = 169\$, which gives n = 13.

### Question 4

What is the value of \$(√4 - 1/√4)^2\$?

A

\$2{1/4}\$.

B

\$2{3/4}\$.

C

\$2{1/3}\$.

D

\$2{1/6}\$.

Soln.
Ans: a

I will give a general solution for any n. \$(√n - 1/√n)^2\$ is same as \$({(√n)^2 - 1}/√n)^2\$ which becomes \$(n - 1)^2/n\$. Putting n = 4, we get \${9/4}\$, which is same as: \$2{1/4}\$.

### Question 5

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

A

\$√44\$.

B

\$√25\$.

C

\$√5\$.

D

\$√65\$.

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 - (5√5)^2}\$, which is same as \$√{169 - (5^2 × 5)}\$, which is same as \$√{169 - 125}\$ = \$√44\$. 