# Square and Cube Roots Quiz Set 020

### Question 1

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 2

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 3

What is cube root of 0.000343?

A

0.07.

B

.343

C

0.007.

D

0.700.

Soln.
Ans: a

We can see that 0.07 × 0.07 × 0.07 = 0.000343, so cube root is 0.07.

### Question 4

What is the value of \$√{3 + √1}\$?

A

2.

B

√3.

C

1.

D

4.

Soln.
Ans: a

The given expression is same as \$√{3 + √1^2}\$, which becomes \$√{3 + 1}\$, or \$√4\$ which gives 2 as the answer. Please note that squares of as many numbers should be always on your tips.

### Question 5

If x = 0.7968, then what is the value of \$4x + √{16x^2 - 8x + 1}\$?

A

1.

B

16.

C

8.

D

2.

Soln.
Ans: a

By inspection, \$4x + √{16x^2 - 8x + 1}\$ is same as \$4x + √{({1 - 4x})^2}\$, which is same as 4x + (1 - 4x) = 1.