Given:
The radical expression is
[tex]\dfrac{1+\sqrt{5}}{\sqrt{2}}[/tex]
To find:
The value of the given expression after rationalizing the denominator.
Solution:
We have,
[tex]\dfrac{1+\sqrt{5}}{\sqrt{2}}[/tex]
Multiply numerator and denominator by [tex]\sqrt{2}[/tex].
[tex]=\dfrac{(1+\sqrt{5})\times \sqrt{2}}{\sqrt{2}\times \sqrt{2}}[/tex]
[tex]=\dfrac{\sqrt{2}+\sqrt{5}\sqrt{2}}{2}[/tex]
[tex]=\dfrac{\sqrt{2}+\sqrt{10}}{2}[/tex] [tex][\because \sqrt{ab}=\sqrt{a}\sqrt{b}][/tex]
Therefore, the required expression after rationalizing the denominator is [tex]\dfrac{\sqrt{2}+\sqrt{10}}{2}[/tex].
