Simplify ( square root of 20x^3)/( square root of 5x)

$\frac{\sqrt{20 x^{3}}}{\sqrt{5 x}}$

Step 1

Combine $\sqrt{20 x^{3}}$ and $\sqrt{5 x}$ into a single radical.

$\sqrt{\frac{20 x^{3}}{5 x}}$

Step 2

Reduce the expression $\frac{20 x^{3}}{5 x}$ by cancelling the common factors.

Factor $5$ out of $20 x^{3}$ .

$\sqrt{\frac{5 (4 x^{3})}{5 x}}$

Factor $5$ out of $5 x$ .

$\sqrt{\frac{5 (4 x^{3})}{5 (x)}}$

Cancel the common factor.

$\sqrt{\frac{5 (4 x^{3})}{5 x}}$

Rewrite the expression.

$\sqrt{\frac{4 x^{3}}{x}}$

Step 3

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

Factor $x$ out of $4 x^{3}$ .

$\sqrt{\frac{x (4 x^{2})}{x}}$

Cancel the common factors.

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

$\sqrt{\frac{x (4 x^{2})}{x^{1}}}$

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

$\sqrt{\frac{x (4 x^{2})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x (4 x^{2})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{4 x^{2}}{1}}$

Divide $4 x^{2}$ by $1$ .

$\sqrt{4 x^{2}}$

Step 4

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

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

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$2 x$