How do you simplify #sqrt(32a^7b^4 )#?

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Answer 1 · 2015-10-09T16:41:16

#4a^3b^2sqrt(2a)#

Since everything under the square root is being multiplied, we can take out things that are squares. Let's break things up one piece at a time:

The #a# variable:

#sqrt(a^7)#
#a^6*a = a^7#
#a^3sqrt(a) = sqrt(a^7)#

The #b# variable:

#sqrt(b^4)#
#b^2 = sqrt(b^4)#

The constant (32):

#sqrt(16*2) = sqrt(32)#
#4sqrt(2) = sqrt(32)#

Now we multiply everything together in order to get our answer.
#4a^3b^2sqrt(2a)#