Question

$\text{By rationalizing the denominator of}\frac{11}{\sqrt{7}},$$\text{we get}$

• A. $\frac{7\sqrt{7}}{11}$
• B. $\frac{11\sqrt{11}}{7}$
• C. $\frac{7\sqrt{11}}{11}$
• D. $\frac{11\sqrt{7}}{7}$

Answer 1

The correct option is D $\frac{11\sqrt{7}}{7}$

The denominator of $\frac{11}{\sqrt{7}}$ is$\sqrt{7}$ which is an irrational number.

To rationalize the denominator, multiply by $\sqrt{7}$ in both numerator and denominator

$\Rightarrow \frac{11}{\sqrt{7}}$
$=\frac{11}{\sqrt{7}}\times \frac{\sqrt{7}}{\sqrt{7}}$
$=\frac{11\times \sqrt{7}}{\sqrt{7\times 7}}$
$=\frac{11\times \sqrt{7}}{\sqrt{7^2}}$
$=\frac{11}{7}\sqrt{7}$

After rationalizing the denominator of $\frac{11}{\sqrt{7}}$, the new expression is $\frac{11}{7}\sqrt{7}$ which contains denominator as the rational number $7$.