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

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Answer 1 · 2015-04-11T19:47:32

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)
$= 2asqrt(6ab)$

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