How do you simplify #sqrt(36a^4b^10)#?

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Answer 1 · 2018-03-02T05:05:02

#6a^2b^5#

#sqrt(36a^4b^10)#

#(36a^4b^10)^(1/2)#

#(36)^(1/2)(a^4)^(1/2)(b^10)^(1/2)#

#sqrt36a^2b^5#

#6a^2b^5#

For your information, taking the square root and raising to the power of #1/2# is the same thing.

For example:

#5^2=25#

#sqrt(5^2)=sqrt25#

#sqrt(5^2)=5#

so that must mean that taking a square root is really taking it to the #1/2# because

#5^(2*1/2)=5#

#5^1=5#

Answer 2 · 2018-03-02T05:05:33

#6a^2b^5#

#sqrt(36a^4b^10) = sqrt36 * sqrt(a^4) * sqrt(b^10)#

#=6*a^2*sqrt((b^5)^2)#

#=6a^2*b^5#

#=6a^2b^5#

Thus, we have our answer.