Question

Simplify the expression:
$\frac{\sqrt{20}+\frac{\sqrt{10}}{\sqrt{18}}}{5^{\frac{1}{2}}}$

Answer 1

As per PEMDAS rule, we need to evaluate exponential followed by divsion and addition.

Let's simplify first by expanding each terms.
$\frac{\sqrt{20}+\frac{\sqrt{10}}{\sqrt{8}}}{5^{\frac{1}{2}}}=\frac{\sqrt{20}+\frac{\sqrt{2\times 5}}{\sqrt{2\times 2\times 2}}}{\sqrt{5}}$
(canceling the common terms)
$=\frac{\sqrt{20}+\frac{\sqrt{5}}{\sqrt{2\times 2}}}{\sqrt{5}}=\frac{\sqrt{4\times 5}+\frac{\sqrt{5}}{2}}{\sqrt{5}}=\frac{2\sqrt{5}+\frac{\sqrt{5}}{2}}{\sqrt{5}}$
(taking $\sqrt{5}$ as common term)
$=\frac{\sqrt{5}(2+\frac{1}{2})}{\sqrt{5}}$
(canceling $\sqrt{5}$ from numerator and denominator)
$=2+\frac{1}{2}$
$=2.5$