Question

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

• A. $6-\sqrt{12}$
• B. $6+\sqrt{35}$
• C. $6+\sqrt{12}$
• D. $6-\sqrt{35}$

Answer 1

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

As givne $\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}$
Now multiplying and divide by $\sqrt{7}-\sqrt{5}$
$=\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\times \frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}-\sqrt{5}}$
$=\frac{{(\sqrt{7}-\sqrt{5})}^2}{{\left(\sqrt{7}\right)}^2-{\left(\sqrt{5}\right)}^2}$
$=\frac{7+5-2\times \sqrt{7}\times \sqrt{5}}{7-5}$
$=\frac{12-2\sqrt{35}}{2}$
$=6-\sqrt{35}$