# Simplify the expression: sqrt(1/(10))+sqrt(5/2)+sqrt(2/5)-sqrt(40)

Simplify the expression:
$\sqrt{\frac{1}{10}}+\sqrt{\frac{5}{2}}+\sqrt{\frac{2}{5}}-\sqrt{40}$
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Christina Matthews
$\sqrt{\frac{1}{10}}+\sqrt{\frac{5}{2}}+\sqrt{\frac{2}{5}}-\sqrt{40}$
$=\frac{1}{\sqrt{10}}+\frac{\sqrt{5}}{\sqrt{2}}+\frac{\sqrt{2}}{\sqrt{5}}-\frac{2\sqrt{10}}{1}$
$=\frac{1+\sqrt{5}\ast \sqrt{5}+\sqrt{2}\ast \sqrt{2}-2\sqrt{10}\ast \sqrt{10}}{\sqrt{10}}=$
$=\frac{1+5+2-2\ast 10}{\sqrt{10}}=$
$=\frac{-12}{\sqrt{10}}=\frac{-12\sqrt{10}}{\sqrt{10}\ast \sqrt{10}}=\frac{-12\sqrt{10}}{10}=\frac{-6\sqrt{10}}{5}$