# Square and Cube Roots Quiz Set 003

### Question 1

Each box of a almirah has as many balls as is the total number of boxes in that almirah. If there are 144 balls in all, how many boxes are there?

A

12.

B

9.

C

16.

D

10.

Soln.
Ans: a

Let the number of boxes = n. So balls in one box are also n, and therefore, balls in n boxes = \$n^2\$. We have been given \$n^2 = 144\$, which gives n = 12.

### Question 2

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

A

1.697.

B

1.414.

C

1.732.

D

0.707.

Soln.
Ans: a

The given expression can be simplified to \${{(√2)^2} - {5 × 2} + {5 × √2 × √{2 × 2^2}}}/{5 × √2}\$, which is same as \${2 - 10 + 20}/{5 × √2}\$, which is same as \${12/{5 × √2}\$. Rationalizing, we get \${12/{5 × √2} × {√2/√2}\$ which gives \${12√2}/10\$ which = 1.697.

### Question 3

If \$√5\$ = 2.24, then what is the value of \${√5}/2\$ − \$3/{√5}\$ + \$√20\$?

A

4.249.

B

4.449.

C

4.649.

D

4.496.

Soln.
Ans: a

The given expression can be simplified to \${{(√5)^2} - {2 × 3} + {2 × √5 × √{5 × 2^2}}}/{2 × √5}\$, which is same as \${5 - 6 + 20}/{2 × √5}\$, which is same as \${19/{2 × √5}\$. Rationalizing, we get \${19/{2 × √5} × {√5/√5}\$ which gives \${19√5}/10\$ which = 4.249.

### Question 4

What is the value of \${√11}/3\$ − \$2/{√11}\$?

A

\${5√11}/33\$.

B

\${15√11}/33\$.

C

\${13√11}/33\$.

D

\${6√11}/33\$.

Soln.
Ans: a

The given expression can be simplified to \${{(√11)^2} - 3 × 2}/{3 × √11}\$, which is same as \${11 - 6}/{3 × √11}\$, which is same as \${5/{3 × √11}\$. Rationalizing, we get \${5/{3 × √11} × {√11/√11}\$ which gives \${5√11}/33\$

### Question 5

If \$√2\$ = 1.41, then what is the value of \${√2}/5\$ − \$5/{√2}\$ + \$√50\$?

A

3.818.

B

-3.818.

C

7.636.

D

-7.636.

Soln.
Ans: a

The given expression can be simplified to \${{(√2)^2} - {5 × 5} + {5 × √2 × √{2 × 5^2}}}/{5 × √2}\$, which is same as \${2 - 25 + 50}/{5 × √2}\$, which is same as \${27/{5 × √2}\$. Rationalizing, we get \${27/{5 × √2} × {√2/√2}\$ which gives \${27√2}/10\$ which = 3.818. This Blog Post/Article "Square and Cube Roots Quiz Set 003" 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