Question

simplify by rationalising the denominator
$\frac{1}{5 + \sqrt{2} }$
​

Answer 1

$\large \frac{1}{5 + \sqrt{2} }$

Multiply the numerator and the denominator with (5 - √2),

$= \large \frac{1}{5 + \sqrt{2} } \times \frac{5 - \sqrt{2} }{5 - \sqrt{2} }$

$= \large \frac{5 - \sqrt{2} }{(5 + \sqrt{2})(5 - \sqrt{2} ) }$

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

$= \large \frac{5 - \sqrt{2} }{ 25 - 2 }$

$= \large \frac{5 - \sqrt{2} }{ 23 }$

Answer 2

Answer:

PLEASE REFER TO THE ATTACHMENT.

Step-by-step explanation:

I HOPE IT'S HELPFUL FOR YOU.