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

1 Answer
Sally
Apr 8, 2015

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)#

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