# How do you simplify sqrt (15x) * (21x)?

May 18, 2015

By exponentiial rules, we know that ${a}^{n} \cdot {a}^{m} = {a}^{n + m}$

So, in this case, if we rewrite your product:

${\left(15 x\right)}^{\frac{1}{2}} \cdot \left(21 x\right) = {15}^{\frac{1}{2}} \cdot {x}^{\frac{1}{2}} \cdot 21 x$

We can sum the exponentials of the variable $x$.

${15}^{\frac{1}{2}} \cdot 21 {x}^{\frac{3}{2}}$

Simpifying more, we can even factor the constants, as both are multplied by three:

${5}^{\frac{1}{2}} \cdot \textcolor{g r e e n}{3 \left(\frac{1}{2}\right)} \cdot 7 \cdot \textcolor{g r e e n}{3} \cdot {x}^{\frac{3}{2}}$

${5}^{\frac{1}{2}} \cdot 7 \cdot {3}^{\frac{3}{2}} \cdot {x}^{\frac{3}{2}}$

Transforming all these exponentials into roots:

$7 \sqrt{5} \sqrt{{\left(3 x\right)}^{3}}$