Simplify the Radical Expression ( cube root of x* square root of x^3)/( square root of 25x)

$\frac{\sqrt[3]{x} \cdot \sqrt{x^{3}}}{\sqrt{25 x}}$

Step 1

Combine $\sqrt{x^{3}}$ and $\sqrt{25 x}$ into a single radical.

$\sqrt[3]{x} \cdot \sqrt{\frac{x^{3}}{25 x}}$

Step 2

Reduce the expression $\frac{x^{3}}{25 x}$ by cancelling the common factors.

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

$\sqrt[3]{x} \cdot \sqrt{\frac{x \cdot x^{2}}{25 x}}$

Factor $x$ out of $25 x$ .

$\sqrt[3]{x} \cdot \sqrt{\frac{x \cdot x^{2}}{x \cdot 25}}$

Cancel the common factor.

$\sqrt[3]{x} \cdot \sqrt{\frac{x \cdot x^{2}}{x \cdot 25}}$

Rewrite the expression.

$\sqrt[3]{x} \cdot \sqrt{\frac{x^{2}}{25}}$

Step 3

Rewrite $25$ as $5^{2}$ .

$\sqrt[3]{x} \cdot \sqrt{\frac{x^{2}}{5^{2}}}$

Step 4

Rewrite $\frac{x^{2}}{5^{2}}$ as ${(\frac{x}{5})}^{2}$ .

$\sqrt[3]{x} \cdot \sqrt{{(\frac{x}{5})}^{2}}$

Step 5

Pull terms out from under the radical.

$\sqrt[3]{x} \cdot | \frac{x}{5} |$

Step 6

Remove non-negative terms from the absolute value.

$\sqrt[3]{x} \cdot \frac{| x |}{5}$

Step 7

Combine $\sqrt[3]{x}$ and $\frac{| x |}{5}$ .

$\frac{\sqrt[3]{x} | x |}{5}$