How do you simplify sqrt (49 m^2n^ 8)?

1 Answer
Mar 27, 2018

7mn^4

Explanation:

First, we know that asqrtbc is the same as asqrtb*asqrtc

Therefore, sqrt49m^2n^8 is the same as sqrt49*sqrtm^2*sqrtn^8

And we know that sqrt49 is 7 so we would have
7sqrtm^2*sqrtn^8

We also know that asqrtb^a is the same as b, so sqrtm^2 is m.

We would now have 7msqrtn^8.

We will apply the rule that asqrtb^c=b^(c/a)

So, 7msqrtn^8=7mn^(8/2) and 8/2 is 4

Final answer: 7mn^4.