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

Jun 23, 2016

Factor it out.

#### Explanation:

Break down the expression into its factors:

$\sqrt{125 {a}^{3}} = \sqrt{5 \cdot 5 \cdot 5 \cdot a \cdot a \cdot a}$

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.

$\sqrt{5 \cdot {\left(5\right)}^{2} \cdot a \cdot \left({a}^{2}\right)} = 5 \cdot a \cdot \sqrt{5 \cdot a}$

Finally,

$5 \cdot a \cdot \sqrt{5 \cdot a} = 5 a \sqrt{5 a}$

$\sqrt{125 {a}^{3}} = 5 a \sqrt{5 a}$

Hope this helps!