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

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Answer 1 · 2018-03-27T12:18:36

#7mn^4#

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#.