# Simplifying fraction containgin square root

Say we have an expression like

$$\frac{\sqrt{\frac{k}{g}}}{k}=\frac{1}{\sqrt{gk}}$$

How do we get from the left hand side, to the right hand side? If we simplify the square root

$$\sqrt{\frac{k}{g}}=\frac{\sqrt{k}}{\sqrt{g}}$$

Then

$$\frac{\sqrt{k}}{\sqrt{g}}\times \frac{1}{k}=\frac{\sqrt{k}}{k\sqrt{g}}$$

Then multiply through by $$\sqrt{k}$$ and cancel out $$k$$?

$$\frac{\sqrt{k}}{k\sqrt{g}}=\frac{k}{k\sqrt{g}\sqrt{k}}=\frac{1}{\sqrt{gk}}$$

Is that correct?

• Yes, that’s right. – KM101 Nov 5 '18 at 15:29

$$\frac{\sqrt{\frac{k}{g}}}{k}=\frac{\sqrt \frac kg}{\sqrt\frac{k^2}{1}}=\sqrt\frac{k \over g}{k^2 \over 1}=\sqrt\frac{k}{gk^2}=\sqrt\frac{1}{gk}={\sqrt{1} \over \sqrt{gk}}={1 \over \sqrt{gk}}$$