Simplify the Radical Expression ( square root of 90x^18)/( square root of 2x)

$\frac{\sqrt{90 x^{18}}}{\sqrt{2 x}}$

Combine $\sqrt{90 x^{18}}$ and $\sqrt{2 x}$ into a single radical.

$\sqrt{\frac{90 x^{18}}{2 x}}$

Reduce the expression $\frac{90 x^{18}}{2 x}$ by cancelling the common factors.

Factor $2$ out of $90 x^{18}$ .

$\sqrt{\frac{2 (45 x^{18})}{2 x}}$

Factor $2$ out of $2 x$ .

$\sqrt{\frac{2 (45 x^{18})}{2 (x)}}$

Cancel the common factor.

$\sqrt{\frac{2 (45 x^{18})}{2 x}}$

Rewrite the expression.

$\sqrt{\frac{45 x^{18}}{x}}$

Cancel the common factor of $x^{18}$ and $x$ .

Factor $x$ out of $45 x^{18}$ .

$\sqrt{\frac{x (45 x^{17})}{x}}$

Cancel the common factors.

Raise $x$ to the power of $1$ .

$\sqrt{\frac{x (45 x^{17})}{x^{1}}}$

Factor $x$ out of $x^{1}$ .

$\sqrt{\frac{x (45 x^{17})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x (45 x^{17})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{45 x^{17}}{1}}$

Divide $45 x^{17}$ by $1$ .

$\sqrt{45 x^{17}}$

Rewrite $45 x^{17}$ as ${(3 x^{8})}^{2} \cdot (5 x)$ .

Factor $9$ out of $45$ .

$\sqrt{9 (5) x^{17}}$

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

$\sqrt{3^{2} \cdot 5 x^{17}}$

Factor out $x^{16}$ .

$\sqrt{3^{2} \cdot 5 (x^{16} x)}$

Rewrite $x^{16}$ as ${(x^{8})}^{2}$ .

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

Move $5$ .

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

Rewrite $3^{2} {(x^{8})}^{2}$ as ${(3 x^{8})}^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

$| 3 x^{8} | \sqrt{5 x}$

Remove non-negative terms from the absolute value.

$3 x^{8} \sqrt{5 x}$