Simplify ( square root of 75x^3)/( square root of 3x)

$\frac{\sqrt{75 x^{3}}}{\sqrt{3 x}}$

Step 1

Combine $\sqrt{75 x^{3}}$ and $\sqrt{3 x}$ into a single radical.

$\sqrt{\frac{75 x^{3}}{3 x}}$

Step 2

Reduce the expression $\frac{75 x^{3}}{3 x}$ by cancelling the common factors.

Factor $3$ out of $75 x^{3}$ .

$\sqrt{\frac{3 (25 x^{3})}{3 x}}$

Factor $3$ out of $3 x$ .

$\sqrt{\frac{3 (25 x^{3})}{3 (x)}}$

Cancel the common factor.

$\sqrt{\frac{3 (25 x^{3})}{3 x}}$

Rewrite the expression.

$\sqrt{\frac{25 x^{3}}{x}}$

Step 3

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

Factor $x$ out of $25 x^{3}$ .

$\sqrt{\frac{x (25 x^{2})}{x}}$

Cancel the common factors.

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

$\sqrt{\frac{x (25 x^{2})}{x^{1}}}$

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

$\sqrt{\frac{x (25 x^{2})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x (25 x^{2})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{25 x^{2}}{1}}$

Divide $25 x^{2}$ by $1$ .

$\sqrt{25 x^{2}}$

Step 4

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

$\sqrt{{(5 x)}^{2}}$

Step 5

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

$5 x$