Simplify 3 square root of 125x^9

$3 \sqrt{125 x^{9}}$

Step 1

Rewrite $125 x^{9}$ as ${(5 x^{4})}^{2} \cdot (5 x)$ .

Factor $25$ out of $125$ .

$3 \sqrt{25 (5) x^{9}}$

Rewrite $25$ as $5^{2}$ .

$3 \sqrt{5^{2} \cdot 5 x^{9}}$

Factor out $x^{8}$ .

$3 \sqrt{5^{2} \cdot 5 (x^{8} x)}$

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$3 \sqrt{5^{2} \cdot 5 ({(x^{4})}^{2} x)}$

Move $5$ .

$3 \sqrt{5^{2} {(x^{4})}^{2} \cdot 5 x}$

Rewrite $5^{2} {(x^{4})}^{2}$ as ${(5 x^{4})}^{2}$ .

$3 \sqrt{{(5 x^{4})}^{2} \cdot 5 x}$

Add parentheses.

$3 \sqrt{{(5 x^{4})}^{2} \cdot (5 x)}$

Step 2

Pull terms out from under the radical.

$3 (5 x^{4} \sqrt{5 x})$

Step 3

Multiply $5$ by $3$ .

$15 x^{4} \sqrt{5 x}$