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

Question

11323 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-04-08T20:46:35

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

$sqrt(512k^2)=sqrt(512)*sqrt(k^2)$
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.

$512/2=256$

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

$sqrt(512k^2)=sqrt(256*2)*sqrt(k^2)=sqrt(256)*sqrt(2)*k=16ksqrt(2)$

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