# How do you simplify sqrt22.5?

I would multiply and divide by $10$:
$\sqrt{\frac{10}{10} \cdot 22.5} = \sqrt{\frac{225}{10}} = \frac{15}{\sqrt{10}}$
let us then rationalize multiplying and dividing by $\sqrt{10}$:
$\frac{15}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}} = \frac{15 \sqrt{10}}{10} = \frac{3}{2} \sqrt{10}$