Simplify ( square root of 200x^3y^4)/( square root of 10xy^4)

$\frac{\sqrt{200 x^{3} y^{4}}}{\sqrt{10 x y^{4}}}$

Step 1

Combine $\sqrt{200 x^{3} y^{4}}$ and $\sqrt{10 x y^{4}}$ into a single radical.

$\sqrt{\frac{200 x^{3} y^{4}}{10 x y^{4}}}$

Step 2

Reduce the expression $\frac{200 x^{3} y^{4}}{10 x y^{4}}$ by cancelling the common factors.

Factor $10$ out of $200 x^{3} y^{4}$ .

$\sqrt{\frac{10 (20 x^{3} y^{4})}{10 x y^{4}}}$

Factor $10$ out of $10 x y^{4}$ .

$\sqrt{\frac{10 (20 x^{3} y^{4})}{10 (x y^{4})}}$

Cancel the common factor.

$\sqrt{\frac{10 (20 x^{3} y^{4})}{10 (x y^{4})}}$

Rewrite the expression.

$\sqrt{\frac{20 x^{3} y^{4}}{x y^{4}}}$

Step 3

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

Factor $x$ out of $20 x^{3} y^{4}$ .

$\sqrt{\frac{x (20 x^{2} y^{4})}{x y^{4}}}$

Cancel the common factors.

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

$\sqrt{\frac{x (20 x^{2} y^{4})}{x (y^{4})}}$

Cancel the common factor.

$\sqrt{\frac{x (20 x^{2} y^{4})}{x y^{4}}}$

Rewrite the expression.

$\sqrt{\frac{20 x^{2} y^{4}}{y^{4}}}$

Step 4

Cancel the common factor of $y^{4}$ .

Cancel the common factor.

$\sqrt{\frac{20 x^{2} y^{4}}{y^{4}}}$

Divide $20 x^{2}$ by $1$ .

$\sqrt{20 x^{2}}$

Step 5

Rewrite $20 x^{2}$ as ${(2 x)}^{2} \cdot 5$ .

Factor $4$ out of $20$ .

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

Rewrite $4$ as $2^{2}$ .

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

Move $5$ .

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

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

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

Step 6

Pull terms out from under the radical.

$2 x \sqrt{5}$