Simplify ( square root of 189x^3y^6)/( square root of 3x)

$\frac{\sqrt{189 x^{3} y^{6}}}{\sqrt{3 x}}$

Combine $\sqrt{189 x^{3} y^{6}}$ and $\sqrt{3 x}$ into a single radical.

$\sqrt{\frac{189 x^{3} y^{6}}{3 x}}$

Reduce the expression $\frac{189 x^{3} y^{6}}{3 x}$ by cancelling the common factors.

Factor $3$ out of $189 x^{3} y^{6}$ .

$\sqrt{\frac{3 (63 x^{3} y^{6})}{3 x}}$

Factor $3$ out of $3 x$ .

$\sqrt{\frac{3 (63 x^{3} y^{6})}{3 (x)}}$

Cancel the common factor.

$\sqrt{\frac{3 (63 x^{3} y^{6})}{3 x}}$

Rewrite the expression.

$\sqrt{\frac{63 x^{3} y^{6}}{x}}$

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

Factor $x$ out of $63 x^{3} y^{6}$ .

$\sqrt{\frac{x (63 x^{2} y^{6})}{x}}$

Cancel the common factors.

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

$\sqrt{\frac{x (63 x^{2} y^{6})}{x^{1}}}$

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

$\sqrt{\frac{x (63 x^{2} y^{6})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x (63 x^{2} y^{6})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{63 x^{2} y^{6}}{1}}$

Divide $63 x^{2} y^{6}$ by $1$ .

$\sqrt{63 x^{2} y^{6}}$

Rewrite $63 x^{2} y^{6}$ as ${(3 x y^{3})}^{2} \cdot 7$ .

Factor $9$ out of $63$ .

$\sqrt{9 (7) x^{2} y^{6}}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 7 x^{2} y^{6}}$

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

$\sqrt{3^{2} \cdot 7 x^{2} {(y^{3})}^{2}}$

Move $7$ .

$\sqrt{3^{2} x^{2} {(y^{3})}^{2} \cdot 7}$

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

$\sqrt{{(3 x y^{3})}^{2} \cdot 7}$

Pull terms out from under the radical.

$3 x y^{3} \sqrt{7}$