Question

Find the value of the given expression =2+1/√2 +1/2+√2 + 1/√2-2

Answer 1

Answer:

$2+\frac{1}{\sqrt{2}}+\frac{1}{2}+\sqrt{2}+\frac{1}{\sqrt{2}}-2=\frac{1}{2}+2\sqrt{2}\quad \left(\mathrm{Decimal:\quad }\:3.32842\dots \right)$

Step-by-step explanation:

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

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

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

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

$\mathrm{Add\:similar\:elements:}\:\sqrt{2}+\sqrt{2}=2\sqrt{2}$

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

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