Simplifying square root with fraction

Question

I'm not sure about this equality $$4(-3+\sqrt {15})/4)^2 = (9-6 \sqrt{15} +15)/4$$

Hope some one can enlighten me. I will be facing more of such fractions, please guide me on how to solve/simplify in easy method.

Thanks :)

Answer 1

I’ll even finish the simplification:

$$\begin{align*} 4\left(\frac{-3+\sqrt{15}}4\right)^2&=4\cdot\frac{(-3+\sqrt{15})(-3+\sqrt{15}}{4\cdot4}\\ &=\frac{(-3)^2+2(-3)\sqrt{15}+(\sqrt{15})^2}4\\ &=\frac{9-6\sqrt{15}+15}4\\ &=\frac{24-6\sqrt{15}}4\\ &=6-\frac32\sqrt{15}\;. \end{align*}$$

In short: cancel a factor of $4$, and multiply out the numerator.