Question

Rationalise the denominator of:
root7 - root5 / root7 + root5

Answer 1

Hi there

Hope this will help you

Thank You

Answer 2

Answer:

$6-\sqrt{35}$

Step-by-step explanation:

Here, the given expression is,

$\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}$

For rationalizing the denominator,

Multiply both numerator and denominator by √7 - √5,

$\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\times \frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}-\sqrt{5}}$

$=\frac{(\sqrt{7}-\sqrt{5})^2}{(\sqrt{7})^2-(\sqrt{5})^2}$

$=\frac{7+5-2\times \sqrt{7}\times \sqrt{5}}{7-5}$

$=\frac{12-2\sqrt{35}}{2}$

$=6-\sqrt{35}$