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

Apr 11, 2015

Remember that $\sqrt{p q} = \sqrt{p} \cdot \sqrt{q}$

So we can "break-up" the given square root:
$\sqrt{24 {a}^{3} b}$

(separate out the different "kinds" of terms within the root)
$= \sqrt{24} \cdot \sqrt{{a}^{2}} \cdot \sqrt{b}$

(extract squares within each root)
$= \sqrt{4} \sqrt{6} \cdot \sqrt{{a}^{2}} \sqrt{a} \cdot \sqrt{b}$

(simplify the square root of squares)
$= 2 \sqrt{6} \cdot a \sqrt{a} \cdot \sqrt{b}$

(recombine for simplicity)
$= 2 a \sqrt{6 a b}$