Simplify (3 square root of 12x^3)/( square root of 75x)

$\frac{3 \sqrt{12 x^{3}}}{\sqrt{75 x}}$

Step 1

Combine $\sqrt{12 x^{3}}$ and $\sqrt{75 x}$ into a single radical.

$3 \sqrt{\frac{12 x^{3}}{75 x}}$

Step 2

Reduce the expression $\frac{12 x^{3}}{75 x}$ by cancelling the common factors.

Factor $3$ out of $12 x^{3}$ .

$3 \sqrt{\frac{3 (4 x^{3})}{75 x}}$

Factor $3$ out of $75 x$ .

$3 \sqrt{\frac{3 (4 x^{3})}{3 (25 x)}}$

Cancel the common factor.

$3 \sqrt{\frac{3 (4 x^{3})}{3 (25 x)}}$

Rewrite the expression.

$3 \sqrt{\frac{4 x^{3}}{25 x}}$

Step 3

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

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

$3 \sqrt{\frac{x (4 x^{2})}{25 x}}$

Cancel the common factors.

Factor $x$ out of $25 x$ .

$3 \sqrt{\frac{x (4 x^{2})}{x \cdot 25}}$

Cancel the common factor.

$3 \sqrt{\frac{x (4 x^{2})}{x \cdot 25}}$

Rewrite the expression.

$3 \sqrt{\frac{4 x^{2}}{25}}$

Step 4

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

$3 \sqrt{\frac{{(2 x)}^{2}}{25}}$

Step 5

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

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

Step 6

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

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

Step 7

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

$3 \frac{2 x}{5}$

Step 8

Multiply $3 \frac{2 x}{5}$ .

Combine $3$ and $\frac{2 x}{5}$ .

$\frac{3 (2 x)}{5}$

Multiply $2$ by $3$ .

$\frac{6 x}{5}$