How do you simplify \sqrt{200} without using a calculator?

Nov 5, 2014

Since

$200 = 2 \cdot 100 = 2 \cdot {10}^{2}$,

we have

$\sqrt{200} = \sqrt{2 \cdot {10}^{2}} = \sqrt{2} \cdot \sqrt{{10}^{2}} = \sqrt{2} \cdot 10 = 10 \sqrt{2}$.

I hope that this was helpful.