Question

Rationalise the denominator(1+5√)/2√plz helpwith working plz

Answer 1

Given:

The radical expression is

$\dfrac{1+\sqrt{5}}{\sqrt{2}}$

To find:

The value of the given expression after rationalizing the denominator.

Solution:

We have,

$\dfrac{1+\sqrt{5}}{\sqrt{2}}$

Multiply numerator and denominator by $\sqrt{2}$.

$=\dfrac{(1+\sqrt{5})\times \sqrt{2}}{\sqrt{2}\times \sqrt{2}}$

$=\dfrac{\sqrt{2}+\sqrt{5}\sqrt{2}}{2}$

$=\dfrac{\sqrt{2}+\sqrt{10}}{2}$         $[\because \sqrt{ab}=\sqrt{a}\sqrt{b}]$

Therefore, the required expression after rationalizing the denominator is $\dfrac{\sqrt{2}+\sqrt{10}}{2}$.