Simplify ( square root of 18x^3y)/( square root of 2x^4y^2)

$\frac{\sqrt{18 x^{3} y}}{\sqrt{2 x^{4} y^{2}}}$

Step 1

Combine $\sqrt{18 x^{3} y}$ and $\sqrt{2 x^{4} y^{2}}$ into a single radical.

$\sqrt{\frac{18 x^{3} y}{2 x^{4} y^{2}}}$

Step 2

Reduce the expression $\frac{18 x^{3} y}{2 x^{4} y^{2}}$ by cancelling the common factors.

Factor $2$ out of $18 x^{3} y$ .

$\sqrt{\frac{2 (9 x^{3} y)}{2 x^{4} y^{2}}}$

Factor $2$ out of $2 x^{4} y^{2}$ .

$\sqrt{\frac{2 (9 x^{3} y)}{2 (x^{4} y^{2})}}$

Cancel the common factor.

$\sqrt{\frac{2 (9 x^{3} y)}{2 (x^{4} y^{2})}}$

Rewrite the expression.

$\sqrt{\frac{9 x^{3} y}{x^{4} y^{2}}}$

Step 3

Cancel the common factor of $x^{3}$ and $x^{4}$ .

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

$\sqrt{\frac{x^{3} (9 y)}{x^{4} y^{2}}}$

Cancel the common factors.

Factor $x^{3}$ out of $x^{4} y^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

Factor $y$ out of $9 y$ .

$\sqrt{\frac{y \cdot 9}{x y^{2}}}$

Cancel the common factors.

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

$\sqrt{\frac{y \cdot 9}{y (x y)}}$

Cancel the common factor.

$\sqrt{\frac{y \cdot 9}{y (x y)}}$

Rewrite the expression.

$\sqrt{\frac{9}{x y}}$

Step 5

Rewrite $\sqrt{\frac{9}{x y}}$ as $\frac{\sqrt{9}}{\sqrt{x y}}$ .

$\frac{\sqrt{9}}{\sqrt{x y}}$

Step 6

Simplify the numerator.

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

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

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

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

Step 7

Multiply $\frac{3}{\sqrt{x y}}$ by $\frac{\sqrt{x y}}{\sqrt{x y}}$ .

$\frac{3}{\sqrt{x y}} \cdot \frac{\sqrt{x y}}{\sqrt{x y}}$

Step 8

Combine and simplify the denominator.

Multiply $\frac{3}{\sqrt{x y}}$ by $\frac{\sqrt{x y}}{\sqrt{x y}}$ .

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

Raise $\sqrt{x y}$ to the power of $1$ .

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

Raise $\sqrt{x y}$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 \sqrt{x y}}{{\sqrt{x y}}^{1 + 1}}$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{x y}}^{2}$ as $x y$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x y}$ as ${(x y)}^{\frac{1}{2}}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify ( square root of 18x^3y)/( square root of 2x^4y^2)

Related Questions

Support LCMGCF.com by disabling your adblocker.