Simplify ( square root of 54x^5y^3)/( square root of 2x^2y)

$\frac{\sqrt{54 x^{5} y^{3}}}{\sqrt{2 x^{2} y}}$

Step 1

Combine $\sqrt{54 x^{5} y^{3}}$ and $\sqrt{2 x^{2} y}$ into a single radical.

$\sqrt{\frac{54 x^{5} y^{3}}{2 x^{2} y}}$

Step 2

Reduce the expression $\frac{54 x^{5} y^{3}}{2 x^{2} y}$ by cancelling the common factors.

Factor $2$ out of $54 x^{5} y^{3}$ .

$\sqrt{\frac{2 (27 x^{5} y^{3})}{2 x^{2} y}}$

Factor $2$ out of $2 x^{2} y$ .

$\sqrt{\frac{2 (27 x^{5} y^{3})}{2 (x^{2} y)}}$

Cancel the common factor.

$\sqrt{\frac{2 (27 x^{5} y^{3})}{2 (x^{2} y)}}$

Rewrite the expression.

$\sqrt{\frac{27 x^{5} y^{3}}{x^{2} y}}$

Step 3

Cancel the common factor of $x^{5}$ and $x^{2}$ .

Factor $x^{2}$ out of $27 x^{5} y^{3}$ .

$\sqrt{\frac{x^{2} (27 x^{3} y^{3})}{x^{2} y}}$

Cancel the common factors.

Factor $x^{2}$ out of $x^{2} y$ .

$\sqrt{\frac{x^{2} (27 x^{3} y^{3})}{x^{2} (y)}}$

Cancel the common factor.

$\sqrt{\frac{x^{2} (27 x^{3} y^{3})}{x^{2} y}}$

Rewrite the expression.

$\sqrt{\frac{27 x^{3} y^{3}}{y}}$

Step 4

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

Factor $y$ out of $27 x^{3} y^{3}$ .

$\sqrt{\frac{y (27 x^{3} y^{2})}{y}}$

Cancel the common factors.

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

$\sqrt{\frac{y (27 x^{3} y^{2})}{y^{1}}}$

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

$\sqrt{\frac{y (27 x^{3} y^{2})}{y \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{y (27 x^{3} y^{2})}{y \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{27 x^{3} y^{2}}{1}}$

Divide $27 x^{3} y^{2}$ by $1$ .

$\sqrt{27 x^{3} y^{2}}$

Step 5

Rewrite $27 x^{3} y^{2}$ as ${(3 x y)}^{2} \cdot (3 x)$ .

Factor $9$ out of $27$ .

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

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

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

Factor out $x^{2}$ .

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

Move $x$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 6

Pull terms out from under the radical.

$3 x y \sqrt{3 x}$

Simplify ( square root of 54x^5y^3)/( square root of 2x^2y)

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