Question

Simplify by rationalizing the denominator $\frac{4}{\sqrt{7}+\sqrt{3}}$

• A. $\sqrt{7}-\sqrt{2}$
• B. $\sqrt{5}-\sqrt{3}$
• C. $\sqrt{7}-\sqrt{5}$
• D. $\sqrt{7}-\sqrt{3}$

Answer 1

The correct option is D $\sqrt{7}-\sqrt{3}$

$\frac{4}{\sqrt{7}+\sqrt{3}}$
The conjugate of$\sqrt{7}+\sqrt{3}$ is $\sqrt{7}-\sqrt{3}$
$=\frac{4}{\sqrt{7}+\sqrt{3}}\times \frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}-\sqrt{3}}$
$=\frac{4(\sqrt{7}-\sqrt{3})}{7-3}$
$=\sqrt{7}-\sqrt{3}$