Simplify the Radical Expression ( square root of 56x^5y^5)/( square root of 7xy)

$\frac{\sqrt{56 x^{5} y^{5}}}{\sqrt{7 x y}}$

Step 1

Combine $\sqrt{56 x^{5} y^{5}}$ and $\sqrt{7 x y}$ into a single radical.

$\sqrt{\frac{56 x^{5} y^{5}}{7 x y}}$

Step 2

Reduce the expression $\frac{56 x^{5} y^{5}}{7 x y}$ by cancelling the common factors.

Factor $7$ out of $56 x^{5} y^{5}$ .

$\sqrt{\frac{7 (8 x^{5} y^{5})}{7 x y}}$

Factor $7$ out of $7 x y$ .

$\sqrt{\frac{7 (8 x^{5} y^{5})}{7 (x y)}}$

Cancel the common factor.

$\sqrt{\frac{7 (8 x^{5} y^{5})}{7 (x y)}}$

Rewrite the expression.

$\sqrt{\frac{8 x^{5} y^{5}}{x y}}$

Step 3

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

Factor $x$ out of $8 x^{5} y^{5}$ .

$\sqrt{\frac{x (8 x^{4} y^{5})}{x y}}$

Cancel the common factors.

Factor $x$ out of $x y$ .

$\sqrt{\frac{x (8 x^{4} y^{5})}{x (y)}}$

Cancel the common factor.

$\sqrt{\frac{x (8 x^{4} y^{5})}{x y}}$

Rewrite the expression.

$\sqrt{\frac{8 x^{4} y^{5}}{y}}$

Step 4

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

Factor $y$ out of $8 x^{4} y^{5}$ .

$\sqrt{\frac{y (8 x^{4} y^{4})}{y}}$

Cancel the common factors.

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

$\sqrt{\frac{y (8 x^{4} y^{4})}{y^{1}}}$

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

$\sqrt{\frac{y (8 x^{4} y^{4})}{y \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{y (8 x^{4} y^{4})}{y \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{8 x^{4} y^{4}}{1}}$

Divide $8 x^{4} y^{4}$ by $1$ .

$\sqrt{8 x^{4} y^{4}}$

Step 5

Rewrite $8 x^{4} y^{4}$ as ${(2 x^{2} y^{2})}^{2} \cdot 2$ .

Factor $4$ out of $8$ .

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

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

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

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

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

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

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

Move $2$ .

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

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

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

Step 6

Pull terms out from under the radical.

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

Step 7

Remove non-negative terms from the absolute value.

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

Simplify the Radical Expression ( square root of 56x^5y^5)/( square root of 7xy)

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