Simplify ( square root of 90x^9y)/( square root of 2x^5y^5)

$\frac{\sqrt{90 x^{9} y}}{\sqrt{2 x^{5} y^{5}}}$

Step 1

Combine $\sqrt{90 x^{9} y}$ and $\sqrt{2 x^{5} y^{5}}$ into a single radical.

$\sqrt{\frac{90 x^{9} y}{2 x^{5} y^{5}}}$

Step 2

Reduce the expression $\frac{90 x^{9} y}{2 x^{5} y^{5}}$ by cancelling the common factors.

Factor $2$ out of $90 x^{9} y$ .

$\sqrt{\frac{2 (45 x^{9} y)}{2 x^{5} y^{5}}}$

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

$\sqrt{\frac{2 (45 x^{9} y)}{2 (x^{5} y^{5})}}$

Cancel the common factor.

$\sqrt{\frac{2 (45 x^{9} y)}{2 (x^{5} y^{5})}}$

Rewrite the expression.

$\sqrt{\frac{45 x^{9} y}{x^{5} y^{5}}}$

Step 3

Cancel the common factor of $x^{9}$ and $x^{5}$ .

Factor $x^{5}$ out of $45 x^{9} y$ .

$\sqrt{\frac{x^{5} (45 x^{4} y)}{x^{5} y^{5}}}$

Cancel the common factors.

Factor $x^{5}$ out of $x^{5} y^{5}$ .

$\sqrt{\frac{x^{5} (45 x^{4} y)}{x^{5} (y^{5})}}$

Cancel the common factor.

$\sqrt{\frac{x^{5} (45 x^{4} y)}{x^{5} y^{5}}}$

Rewrite the expression.

$\sqrt{\frac{45 x^{4} y}{y^{5}}}$

Step 4

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

Factor $y$ out of $45 x^{4} y$ .

$\sqrt{\frac{y (45 x^{4})}{y^{5}}}$

Cancel the common factors.

Factor $y$ out of $y^{5}$ .

$\sqrt{\frac{y (45 x^{4})}{y \cdot y^{4}}}$

Cancel the common factor.

$\sqrt{\frac{y (45 x^{4})}{y \cdot y^{4}}}$

Rewrite the expression.

$\sqrt{\frac{45 x^{4}}{y^{4}}}$

Step 5

Rewrite $\frac{45 x^{4}}{y^{4}}$ as ${(\frac{3 x^{2}}{y^{2}})}^{2} \cdot 5$ .

Factor the perfect power ${(3 x^{2})}^{2}$ out of $45 x^{4}$ .

$\sqrt{\frac{{(3 x^{2})}^{2} \cdot 5}{y^{4}}}$

Factor the perfect power ${(y^{2})}^{2}$ out of $y^{4}$ .

$\sqrt{\frac{{(3 x^{2})}^{2} \cdot 5}{{(y^{2})}^{2} \cdot 1}}$

Rearrange the fraction $\frac{{(3 x^{2})}^{2} \cdot 5}{{(y^{2})}^{2} \cdot 1}$ .

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

Step 6

Pull terms out from under the radical.

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

Step 7

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

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

Simplify ( square root of 90x^9y)/( square root of 2x^5y^5)

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