# Square and Cube Roots Quiz Set 006

### Question 1

What is the value of \$(√8 - 1/√8)^2\$?

A

\$6{1/8}\$.

B

\$6{1/4}\$.

C

\$6{3/4}\$.

D

\$6{1/3}\$.

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 = 8, we get \${49/8}\$, which is same as: \$6{1/8}\$.

### Question 2

What is the value of \$x\$ in \$√{0.0025 × x}\$ = 0.5?

A

100.

B

10.

C

1000.

D

10000.

Soln.
Ans: a

The given expression can be simplified to \$0.0025 × x\$ = \$0.5^2\$, which gives x = \${0.5^2}/0.0025\$, which is same as \$0.25/0.0025\$ which gives 100.

### Question 3

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 4

What is the value of \${√11}/6\$ − \$3/{√11}\$?

A

\${-7√11}/66\$.

B

\${+7√11}/66\$.

C

\${-3√11}/66\$.

D

\${+3√11}/66\$.

Soln.
Ans: a

The given expression can be simplified to \${{(√11)^2} - 6 × 3}/{6 × √11}\$, which is same as \${11 - 18}/{6 × √11}\$, which is same as \${-7/{6 × √11}\$. Rationalizing, we get \${-7/{6 × √11} × {√11/√11}\$ which gives \${-7√11}/66\$

### Question 5

What is the value of \$√{7 + √1764}\$?

A

7.

B

8.

C

14.

D

6.

Soln.
Ans: a

The given expression is same as \$√{7 + √42^2}\$, which becomes \$√{7 + 42}\$, or \$√49\$ which gives 7 as the answer. Please note that squares of as many numbers should be always on your tips. 