Question

Why √2+√1/2= 3/2√2 ???

Answer 1

we are given with the expression to simplify

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

This can be simplified as below

$\sqrt{2} +\frac{1}{\sqrt{2}}=\sqrt{2} +\frac{1}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}} \\ \\ on \ simplification \ we \ get\\ \\ \sqrt{2} +\frac{1}{\sqrt{2}}=\sqrt{2} +\frac{\sqrt{2}}{2} \\ \\ Now \ add \ the \ terms \ on \ right \ side\\ \\ \sqrt{2} +\frac{1}{\sqrt{2}}=\frac{2\sqrt{2}+\sqrt{2}}{2} \\ \\ Simplify\\ \\ \sqrt{2} +\frac{1}{\sqrt{2}}=\frac{3\sqrt{2}}{2}$