Question

Simplify the following:

${\displaystyle \frac{3}{\sqrt{8}}+\frac{1}{\sqrt{2}}}$

Answer 1

${\displaystyle \frac{3}{\sqrt{8}}+\frac{1}{\sqrt{2}}=\frac{3}{\sqrt{2\times 2\times 2}}+\frac{1}{\sqrt{2}}}$

= ${\displaystyle \frac{3}{2\sqrt{2}}+\frac{1}{\sqrt{2}}}$

= ${\displaystyle \frac{3+2}{2\sqrt{2}}}$

= ${\displaystyle \frac{5}{2\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}}$  ...[Multiplying numerator and denominator by ${\displaystyle \sqrt{2}}$]

= ${\displaystyle \frac{5\sqrt{2}}{2\times 2}}$

= ${\displaystyle \frac{5\sqrt{2}}{4}}$