How do you simplify #sqrt(125a^3)#?

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Answer 1 · 2016-06-23T06:42:22

Factor it out.

Break down the expression into its factors:

#sqrt(125a^3)=sqrt(5*5*5*a*a*a)#

Notice that we have a pair of #5#'s and #a#'s.

#sqrt(5*5*5*a*a*a)=sqrt(5*(5*5)•a*(a*a)) =sqrt(5*(5)^2*a*(a^2))#

We can take these (the pairs) out of the expression.

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

Finally,

#5*a*sqrt(5*a)=5a sqrt(5a)#

#sqrt(125a^3)=5a sqrt(5a)#

Hope this helps!