Simplifying/rewriting a symbolic square root expression

Question

Can someone explain the steps in the below simplification:

$\sqrt{\frac{1}{9} -4\phi } = \frac{1}{3}\sqrt{1 -36\phi } $

How do you get the one third outside of the square root?

Answer 1

$$\sqrt{\frac19-4\phi}=\sqrt{\frac{1-36\phi}{9}}=\frac{\sqrt{1-36\phi}}{\sqrt{9}}$$

Answer 2

Remember that whenever you multiply by $a$, you have to also divide by $a$ to get your original number. Since we see that $\sqrt{1-36\phi}$ is bigger than $\sqrt{\frac{1}{9}-4\phi}$ by a factor of $\sqrt{9}$, we have to divide by $\sqrt{9}$ to get our original answer back.

We can apply this principle in the following steps:

$$\sqrt{\frac{1}{9}-4\phi} = (\sqrt{\frac{1}{9}-4\phi} \times \sqrt{9} ) \times \frac{1}{\sqrt{9}}$$ $$\Rightarrow \sqrt{1-4\phi} \times \frac{1}{\sqrt{9}}$$ $$\Rightarrow \frac{1}{3} \times \sqrt{1-4\phi}$$