<s>[INST] 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?
 [/INST] $$\frac{\sqrt{\frac{k}{g}}}{k}=\frac{\sqrt \frac kg}{\sqrt\frac{k^2}{1}}=\sqrt\frac{k \over g}{k^2 \over 1}=\sqrt\frac{k}{gk^2}=\sqrt\frac{1}{gk}={\sqrt{1} \over 
\sqrt{gk}}={1 \over \sqrt{gk}}$$
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