# Square and Cube Roots Quiz Set 008

### Question 1

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

A

\${-7√11}/66\$.

B

\${+7√11}/66\$.

C

\${-11√7}/66\$.

D

\${-18√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 2

What is the value of \$x\$ in \$√{0.0064 × x}\$ = 0.8?

A

100.

B

8.

C

80.

D

0.8.

Soln.
Ans: a

The given expression can be simplified to \$0.0064 × x\$ = \$0.8^2\$, which gives x = \${0.8^2}/0.0064\$, which is same as \$0.64/0.0064\$ which gives 100.

### Question 3

If x = 0.5356, then what is the value of \$9x + √{4x^2 - 4x + 1}\$?

A

4.75.

B

4.50.

C

4.25.

D

5.00

Soln.
Ans: a

By inspection, \$9x + √{4x^2 - 4x + 1}\$ is same as \$9x + √{({1 - 2x})^2}\$, which is same as 9x + (1 - 2x) = 1 + 7x = 4.75.

### Question 4

If \$4√3 + √27 = 12.12\$, then what is the value of \$√12 + 5√3\$?

A

12.12.

B

12.00.

C

11.12.

D

12.96.

Soln.
Ans: a

The given expression can be rearranged like this: \$4√3 + √{3^{2} × 3}\$, which is same as \$4√3 + 3√3\$ which is same as \$7√3 = 12.12\$, from which we get \$√3 = 1.73\$. Next we can see that \$√12 + 5√3\$ is same as \$√{2^{2} × 3} + 5√3\$, which is same as \$7√3\$, which gives \$7 × 1.73\$ = 12.12.

### Question 5

If \$√2\$ = 1.41, then what is the value of \${√2}/5\$ − \$9/{√2}\$?

A

-6.081.

B

-3.042.

C

+6.081.

D

+3.042.

Soln.
Ans: a

The given expression can be simplified to \${{(√2)^2} - 5 × 9}/{5 × √2}\$, which is same as \${2 - 45}/{5 × √2}\$, which is same as \${-43/{5 × √2}\$. Rationalizing, we get \${-43/{5 × √2} × {√2/√2}\$ which gives \${-43√2}/10\$ which = -6.081.