Simplify square root of 28x^5

$\sqrt{28 x^{5}}$

Step 1

Rewrite $28 x^{5}$ as ${(2 x^{2})}^{2} \cdot (7 x)$ .

Factor $4$ out of $28$ .

$\sqrt{4 (7) x^{5}}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 7 x^{5}}$

Factor out $x^{4}$ .

$\sqrt{2^{2} \cdot 7 (x^{4} x)}$

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

$\sqrt{2^{2} \cdot 7 ({(x^{2})}^{2} x)}$

Move $7$ .

$\sqrt{2^{2} {(x^{2})}^{2} \cdot 7 x}$

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

$\sqrt{{(2 x^{2})}^{2} \cdot 7 x}$

Add parentheses.

$\sqrt{{(2 x^{2})}^{2} \cdot (7 x)}$

Step 2

Pull terms out from under the radical.

$2 x^{2} \sqrt{7 x}$