Simplify the Radical Expression ( square root of 40x^5)/( square root of 10x)

$\frac{\sqrt{40 x^{5}}}{\sqrt{10 x}}$

Combine $\sqrt{40 x^{5}}$ and $\sqrt{10 x}$ into a single radical.

$\sqrt{\frac{40 x^{5}}{10 x}}$

Reduce the expression $\frac{40 x^{5}}{10 x}$ by cancelling the common factors.

Factor $10$ out of $40 x^{5}$ .

$\sqrt{\frac{10 (4 x^{5})}{10 x}}$

Factor $10$ out of $10 x$ .

$\sqrt{\frac{10 (4 x^{5})}{10 (x)}}$

Cancel the common factor.

$\sqrt{\frac{10 (4 x^{5})}{10 x}}$

Rewrite the expression.

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

Cancel the common factor of $x^{5}$ and $x$ .

Factor $x$ out of $4 x^{5}$ .

$\sqrt{\frac{x (4 x^{4})}{x}}$

Cancel the common factors.

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

$\sqrt{\frac{x (4 x^{4})}{x^{1}}}$

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

$\sqrt{\frac{x (4 x^{4})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x (4 x^{4})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{4 x^{4}}{1}}$

Divide $4 x^{4}$ by $1$ .

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

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

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

Pull terms out from under the radical.

$| 2 x^{2} |$

Remove non-negative terms from the absolute value.

$2 x^{2}$