Simplify square root of (90x^9)/(5x^3)

$\sqrt{\frac{90 x^{9}}{5 x^{3}}}$

Reduce the expression $\frac{90 x^{9}}{5 x^{3}}$ by cancelling the common factors.

Factor $5$ out of $90 x^{9}$ .

$\sqrt{\frac{5 (18 x^{9})}{5 x^{3}}}$

Factor $5$ out of $5 x^{3}$ .

$\sqrt{\frac{5 (18 x^{9})}{5 (x^{3})}}$

Cancel the common factor.

$\sqrt{\frac{5 (18 x^{9})}{5 x^{3}}}$

Rewrite the expression.

$\sqrt{\frac{18 x^{9}}{x^{3}}}$

Cancel the common factor of $x^{9}$ and $x^{3}$ .

Factor $x^{3}$ out of $18 x^{9}$ .

$\sqrt{\frac{x^{3} (18 x^{6})}{x^{3}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{x^{3} (18 x^{6})}{x^{3} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x^{3} (18 x^{6})}{x^{3} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{18 x^{6}}{1}}$

Divide $18 x^{6}$ by $1$ .

$\sqrt{18 x^{6}}$

Rewrite $18 x^{6}$ as ${(3 x^{3})}^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\sqrt{9 (2) x^{6}}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 2 x^{6}}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

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

Move $2$ .

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

Rewrite $3^{2} {(x^{3})}^{2}$ as ${(3 x^{3})}^{2}$ .

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

Pull terms out from under the radical.

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