Simplify ( square root of 448x^3y^5)/( square root of 4x^3y)

$\frac{\sqrt{448 x^{3} y^{5}}}{\sqrt{4 x^{3} y}}$

Step 1

Combine $\sqrt{448 x^{3} y^{5}}$ and $\sqrt{4 x^{3} y}$ into a single radical.

$\sqrt{\frac{448 x^{3} y^{5}}{4 x^{3} y}}$

Step 2

Reduce the expression $\frac{448 x^{3} y^{5}}{4 x^{3} y}$ by cancelling the common factors.

Factor $4$ out of $448 x^{3} y^{5}$ .

$\sqrt{\frac{4 (112 x^{3} y^{5})}{4 x^{3} y}}$

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

$\sqrt{\frac{4 (112 x^{3} y^{5})}{4 (x^{3} y)}}$

Cancel the common factor.

$\sqrt{\frac{4 (112 x^{3} y^{5})}{4 (x^{3} y)}}$

Rewrite the expression.

$\sqrt{\frac{112 x^{3} y^{5}}{x^{3} y}}$

Step 3

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

Cancel the common factor.

$\sqrt{\frac{112 x^{3} y^{5}}{x^{3} y}}$

Rewrite the expression.

$\sqrt{\frac{112 y^{5}}{y}}$

Step 4

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

Factor $y$ out of $112 y^{5}$ .

$\sqrt{\frac{y (112 y^{4})}{y}}$

Cancel the common factors.

Raise $y$ to the power of $1$ .

$\sqrt{\frac{y (112 y^{4})}{y^{1}}}$

Factor $y$ out of $y^{1}$ .

$\sqrt{\frac{y (112 y^{4})}{y \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{y (112 y^{4})}{y \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{112 y^{4}}{1}}$

Divide $112 y^{4}$ by $1$ .

$\sqrt{112 y^{4}}$

Step 5

Rewrite $112 y^{4}$ as ${(4 y^{2})}^{2} \cdot 7$ .

Factor $16$ out of $112$ .

$\sqrt{16 (7) y^{4}}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 7 y^{4}}$

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

$\sqrt{4^{2} \cdot 7 {(y^{2})}^{2}}$

Move $7$ .

$\sqrt{4^{2} {(y^{2})}^{2} \cdot 7}$

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

$\sqrt{{(4 y^{2})}^{2} \cdot 7}$

Step 6

Pull terms out from under the radical.

$4 y^{2} \sqrt{7}$

Simplify ( square root of 448x^3y^5)/( square root of 4x^3y)

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