How do you simplify #sqrt(24a^3b)#?

1 Answer
Alan P.
Apr 11, 2015

Remember that #sqrt(pq) = sqrt(p) * sqrt(q)#

So we can "break-up" the given square root:
#sqrt(24a^3b)#

(separate out the different "kinds" of terms within the root)
#= sqrt(24) * sqrt(a^2) * sqrt(b)#

(extract squares within each root)
#= sqrt(4)sqrt(6) * sqrt(a^2)sqrt(a) * sqrt(b)#

(simplify the square root of squares)
#= 2sqrt(6) * asqrt(a) * sqrt(b)#

(recombine for simplicity)
#= 2asqrt(6ab)#

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