Simplify ( square root of 7x)^3

${(\sqrt{7 x})}^{3}$

Step 1

Rewrite ${\sqrt{7 x}}^{3}$ as $\sqrt{{(7 x)}^{3}}$ .

$\sqrt{{(7 x)}^{3}}$

Step 2

Apply the product rule to $7 x$ .

$\sqrt{7^{3} x^{3}}$

Step 3

Raise $7$ to the power of $3$ .

$\sqrt{343 x^{3}}$

Step 4

Rewrite $343 x^{3}$ as ${(7 x)}^{2} \cdot (7 x)$ .

Factor $49$ out of $343$ .

$\sqrt{49 (7) x^{3}}$

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} \cdot 7 x^{3}}$

Factor out $x^{2}$ .

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

Move $7$ .

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

Rewrite $7^{2} x^{2}$ as ${(7 x)}^{2}$ .

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

Add parentheses.

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

Step 5

Pull terms out from under the radical.

$7 x \sqrt{7 x}$