Simplify ( square root of 625x^9y^2)/( square root of 5x^4)

$\frac{\sqrt{625 x^{9} y^{2}}}{\sqrt{5 x^{4}}}$

Step 1

Combine $\sqrt{625 x^{9} y^{2}}$ and $\sqrt{5 x^{4}}$ into a single radical.

$\sqrt{\frac{625 x^{9} y^{2}}{5 x^{4}}}$

Step 2

Reduce the expression $\frac{625 x^{9} y^{2}}{5 x^{4}}$ by cancelling the common factors.

Factor $5$ out of $625 x^{9} y^{2}$ .

$\sqrt{\frac{5 (125 x^{9} y^{2})}{5 x^{4}}}$

Factor $5$ out of $5 x^{4}$ .

$\sqrt{\frac{5 (125 x^{9} y^{2})}{5 (x^{4})}}$

Cancel the common factor.

$\sqrt{\frac{5 (125 x^{9} y^{2})}{5 x^{4}}}$

Rewrite the expression.

$\sqrt{\frac{125 x^{9} y^{2}}{x^{4}}}$

Step 3

Cancel the common factor of $x^{9}$ and $x^{4}$ .

Factor $x^{4}$ out of $125 x^{9} y^{2}$ .

$\sqrt{\frac{x^{4} (125 x^{5} y^{2})}{x^{4}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{x^{4} (125 x^{5} y^{2})}{x^{4} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x^{4} (125 x^{5} y^{2})}{x^{4} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{125 x^{5} y^{2}}{1}}$

Divide $125 x^{5} y^{2}$ by $1$ .

$\sqrt{125 x^{5} y^{2}}$

Step 4

Rewrite $125 x^{5} y^{2}$ as ${(5 x^{2} y)}^{2} \cdot (5 x)$ .

Factor $25$ out of $125$ .

$\sqrt{25 (5) x^{5} y^{2}}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 5 x^{5} y^{2}}$

Factor out $x^{4}$ .

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

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Move $x$ .

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

Move $5$ .

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

Rewrite $(5^{2} ({(x^{2})}^{2})) y^{2}$ as ${(5 x^{2} y)}^{2}$ .

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

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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

Simplify ( square root of 625x^9y^2)/( square root of 5x^4)

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