Simplify 4 square root of 50x^5

$4 \sqrt{50 x^{5}}$

Step 1

Rewrite $50 x^{5}$ as ${(5 x^{2})}^{2} \cdot (2 x)$ .

Factor $25$ out of $50$ .

$4 \sqrt{25 (2) x^{5}}$

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

$4 \sqrt{5^{2} \cdot 2 x^{5}}$

Factor out $x^{4}$ .

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

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

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $5$ by $4$ .

$20 x^{2} \sqrt{2 x}$