Basic Math Examples

$\frac{\sqrt{56 z^{5} y^{6}}}{\sqrt{2 y^{4}}}$

Step 1

Combine $\sqrt{56 z^{5} y^{6}}$ and $\sqrt{2 y^{4}}$ into a single radical.

$\sqrt{\frac{56 z^{5} y^{6}}{2 y^{4}}}$

Step 2

Reduce the expression $\frac{56 z^{5} y^{6}}{2 y^{4}}$ by cancelling the common factors.

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Step 2.1

Factor $2$ out of $56 z^{5} y^{6}$ .

$\sqrt{\frac{2 (28 z^{5} y^{6})}{2 y^{4}}}$

Step 2.2

Factor $2$ out of $2 y^{4}$ .

$\sqrt{\frac{2 (28 z^{5} y^{6})}{2 (y^{4})}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{2 (28 z^{5} y^{6})}{2 y^{4}}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{28 z^{5} y^{6}}{y^{4}}}$

Step 3

Cancel the common factor of $y^{6}$ and $y^{4}$ .

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Step 3.1

Factor $y^{4}$ out of $28 z^{5} y^{6}$ .

$\sqrt{\frac{y^{4} (28 z^{5} y^{2})}{y^{4}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\sqrt{\frac{y^{4} (28 z^{5} y^{2})}{y^{4} \cdot 1}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{y^{4} (28 z^{5} y^{2})}{y^{4} \cdot 1}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{28 z^{5} y^{2}}{1}}$

Step 3.2.4

Divide $28 z^{5} y^{2}$ by $1$ .

$\sqrt{28 z^{5} y^{2}}$

Step 4

Rewrite $28 z^{5} y^{2}$ as ${(2 z^{2} y)}^{2} \cdot (7 z)$ .

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Step 4.1

Factor $4$ out of $28$ .

$\sqrt{4 (7) z^{5} y^{2}}$

Step 4.2

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

$\sqrt{2^{2} \cdot 7 z^{5} y^{2}}$

Step 4.3

Factor out $z^{4}$ .

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

Step 4.4

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

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

Step 4.5

Move $z$ .

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

Step 4.6

Move $7$ .

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

Step 4.7

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

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

Step 4.8

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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