# What is the square root of 12.5?

I found: $5 \frac{\sqrt{2}}{2}$
$12.5 = \frac{125}{10}$ so:
$\sqrt{12.5} = \sqrt{\frac{125}{10}} = \frac{\sqrt{125}}{\sqrt{10}} = \frac{\sqrt{5 \cdot 25}}{\sqrt{5 \cdot 2}} =$
$5 \frac{\sqrt{5}}{\sqrt{5} \sqrt{2}} = \frac{5}{\sqrt{2}} =$ rationalizing:
$= 5 \frac{\sqrt{2}}{2}$