Simplifying $\frac{\frac12\sqrt{w^2+d^2}}{\sqrt{\frac14(w^2+d^2)+(h-k)^2}}$ to $\sqrt{\frac{w^2+d^2}{d^2+4(h-k)^2+w^2}}$

Question

I'm getting to the point in an example question where I get the answer:

$$\frac{\frac12\sqrt{w^2+d^2}}{\sqrt{\frac14(w^2+d^2)+(h-k)^2}}\quad\to\quad\sqrt{\frac{w^2+d^2}{d^2+4(h-k)^2+w^2}}$$

I am having a mental block on how the answer simplified into the second expression.

Answer 1

Multiply the numerator by $2$ and the denominator by $\sqrt{4}$.

That does not change the value, since $2=\sqrt4$, and remember that $\sqrt4\sqrt s=\sqrt{4s}$.