Simplify ( square root of 200x^3y)/( square root of 2xy^5)

$\frac{\sqrt{200 x^{3} y}}{\sqrt{2 x y^{5}}}$

Step 1

Combine $\sqrt{200 x^{3} y}$ and $\sqrt{2 x y^{5}}$ into a single radical.

$\sqrt{\frac{200 x^{3} y}{2 x y^{5}}}$

Step 2

Reduce the expression $\frac{200 x^{3} y}{2 x y^{5}}$ by cancelling the common factors.

Factor $2$ out of $200 x^{3} y$ .

$\sqrt{\frac{2 (100 x^{3} y)}{2 x y^{5}}}$

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

$\sqrt{\frac{2 (100 x^{3} y)}{2 (x y^{5})}}$

Cancel the common factor.

$\sqrt{\frac{2 (100 x^{3} y)}{2 (x y^{5})}}$

Rewrite the expression.

$\sqrt{\frac{100 x^{3} y}{x y^{5}}}$

Step 3

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

Factor $x$ out of $100 x^{3} y$ .

$\sqrt{\frac{x (100 x^{2} y)}{x y^{5}}}$

Cancel the common factors.

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

$\sqrt{\frac{x (100 x^{2} y)}{x (y^{5})}}$

Cancel the common factor.

$\sqrt{\frac{x (100 x^{2} y)}{x y^{5}}}$

Rewrite the expression.

$\sqrt{\frac{100 x^{2} y}{y^{5}}}$

Step 4

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

Factor $y$ out of $100 x^{2} y$ .

$\sqrt{\frac{y (100 x^{2})}{y^{5}}}$

Cancel the common factors.

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

$\sqrt{\frac{y (100 x^{2})}{y \cdot y^{4}}}$

Cancel the common factor.

$\sqrt{\frac{y (100 x^{2})}{y \cdot y^{4}}}$

Rewrite the expression.

$\sqrt{\frac{100 x^{2}}{y^{4}}}$

Step 5

Rewrite $100 x^{2}$ as ${(10 x)}^{2}$ .

$\sqrt{\frac{{(10 x)}^{2}}{y^{4}}}$

Step 6

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

$\sqrt{\frac{{(10 x)}^{2}}{{(y^{2})}^{2}}}$

Step 7

Rewrite $\frac{{(10 x)}^{2}}{{(y^{2})}^{2}}$ as ${(\frac{10 x}{y^{2}})}^{2}$ .

$\sqrt{{(\frac{10 x}{y^{2}})}^{2}}$

Step 8

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

$\frac{10 x}{y^{2}}$

Simplify ( square root of 200x^3y)/( square root of 2xy^5)

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