# How do you simplify sqrt(512k^2)??

Apr 8, 2015

To simplify this, it is helpful to split up what we have

$\sqrt{512 {k}^{2}} = \sqrt{512} \cdot \sqrt{{k}^{2}}$
We can see that the second part becomes just $k$.

Let's look at $\sqrt{512}$ and try to find factors that multiply to give 512. Well, let's start by dividing by 2.

$\frac{512}{2} = 256$

256 is a perfect sqaure! It has factors $16 \cdot 16$. However, 512 is not a perfect square. But we can simplify.

$\sqrt{512 {k}^{2}} = \sqrt{256 \cdot 2} \cdot \sqrt{{k}^{2}} = \sqrt{256} \cdot \sqrt{2} \cdot k = 16 k \sqrt{2}$