How do you simplify 3sqrt.8 - 1sqrt.2?

May 20, 2015

This expression cannot be simplified further without the use of a calculator.

Using a calculator:

$3 \sqrt{.8} - 1 \sqrt{.2}$ =

$\left(3 \times 0.894427191\right) - \left(1 \times 0.4472135955\right) = 2.2360679775$

May 20, 2015

You could actually get this to a simpler form.

$E = 3 \sqrt{.8} - \sqrt{.2}$

$E = 3 \sqrt{\frac{8}{10}} - \sqrt{\frac{2}{10}} = 3 \frac{\sqrt{8}}{\sqrt{10}} - \frac{\sqrt{2}}{\sqrt{10}}$

$E = \frac{1}{\sqrt{10}} \cdot \left(3 \sqrt{8} - \sqrt{2}\right) | \cdot \frac{\sqrt{10}}{\sqrt{10}}$

$E = \frac{\sqrt{10}}{\underbrace{\sqrt{10} \cdot \sqrt{10}}} _ \left(\textcolor{b l u e}{\text{=10}}\right) \cdot \left(3 \sqrt{4 \cdot 2} - \sqrt{2}\right)$

$E = \frac{\sqrt{10}}{10} \cdot \left(3 \cdot 2 \sqrt{2} - \sqrt{2}\right) = \frac{\sqrt{10}}{\stackrel{\textcolor{b l u e}{2}}{\cancel{10}}} \cdot \cancel{5} \sqrt{2}$

$E = \frac{\sqrt{10} \cdot \sqrt{2}}{2} = \frac{\sqrt{20}}{2}$

Using a calculator will indeed give you

$E = 2.236067 \ldots$