Simplify (6 square root of 45x^3)/(3 square root of 5x)

$\frac{6 \sqrt{45 x^{3}}}{3 \sqrt{5 x}}$

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 \sqrt{45 x^{3}}$ .

$\frac{3 (2 \sqrt{45 x^{3}})}{3 \sqrt{5 x}}$

Cancel the common factors.

Factor $3$ out of $3 \sqrt{5 x}$ .

$\frac{3 (2 \sqrt{45 x^{3}})}{3 (\sqrt{5 x})}$

Cancel the common factor.

$\frac{3 (2 \sqrt{45 x^{3}})}{3 \sqrt{5 x}}$

Rewrite the expression.

$\frac{2 \sqrt{45 x^{3}}}{\sqrt{5 x}}$

Combine $\sqrt{45 x^{3}}$ and $\sqrt{5 x}$ into a single radical.

$2 \sqrt{\frac{45 x^{3}}{5 x}}$

Reduce the expression $\frac{45 x^{3}}{5 x}$ by cancelling the common factors.

Factor $5$ out of $45 x^{3}$ .

$2 \sqrt{\frac{5 (9 x^{3})}{5 x}}$

Factor $5$ out of $5 x$ .

$2 \sqrt{\frac{5 (9 x^{3})}{5 (x)}}$

Cancel the common factor.

$2 \sqrt{\frac{5 (9 x^{3})}{5 x}}$

Rewrite the expression.

$2 \sqrt{\frac{9 x^{3}}{x}}$

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

Factor $x$ out of $9 x^{3}$ .

$2 \sqrt{\frac{x (9 x^{2})}{x}}$

Cancel the common factors.

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

$2 \sqrt{\frac{x (9 x^{2})}{x^{1}}}$

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

$2 \sqrt{\frac{x (9 x^{2})}{x \cdot 1}}$

Cancel the common factor.

$2 \sqrt{\frac{x (9 x^{2})}{x \cdot 1}}$

Rewrite the expression.

$2 \sqrt{\frac{9 x^{2}}{1}}$

Divide $9 x^{2}$ by $1$ .

$2 \sqrt{9 x^{2}}$

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

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

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

$2 (3 x)$

Multiply $3$ by $2$ .

$6 x$