Question

Simplify by rationalizing the denominator $\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}$

• A. $6-\sqrt{5}$
• B. $65-\sqrt{35}$
• C. $6-\sqrt{35}$
• D. $6-\sqrt{25}$

Answer 1

The correct option is C $6-\sqrt{35}$

$\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}$
The conjugate of $\sqrt{7}+\sqrt{5}$ is$\sqrt{7}-\sqrt{5}$
$=\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\times \frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}-\sqrt{5}}$
$=\frac{(\sqrt{7}-\sqrt{5}{)}^2}{7-5}$
$=\frac{7+5-2\sqrt{7}\sqrt{5}}{2}$
$=\frac{12-2\sqrt{35}}{2}=6-\sqrt{35}$