Finite Math Examples

$\sqrt{\frac{16 x^{3} y^{7}}{4 z^{6}}}$

Step 1

Reduce the expression $\frac{16 x^{3} y^{7}}{4 z^{6}}$ by cancelling the common factors.

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Step 1.1

Factor $4$ out of $16 x^{3} y^{7}$ .

$\sqrt{\frac{4 (4 x^{3} y^{7})}{4 z^{6}}}$

Step 1.2

Factor $4$ out of $4 z^{6}$ .

$\sqrt{\frac{4 (4 x^{3} y^{7})}{4 (z^{6})}}$

Step 1.3

Cancel the common factor.

$\sqrt{\frac{4 (4 x^{3} y^{7})}{4 z^{6}}}$

Step 1.4

Rewrite the expression.

$\sqrt{\frac{4 x^{3} y^{7}}{z^{6}}}$

Step 2

Rewrite $\frac{4 x^{3} y^{7}}{z^{6}}$ as ${(\frac{2 x y^{3}}{z^{3}})}^{2} (x y)$ .

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Step 2.1

Factor the perfect power ${(2 x y^{3})}^{2}$ out of $4 x^{3} y^{7}$ .

$\sqrt{\frac{{(2 x y^{3})}^{2} (x y)}{z^{6}}}$

Step 2.2

Factor the perfect power ${(z^{3})}^{2}$ out of $z^{6}$ .

$\sqrt{\frac{{(2 x y^{3})}^{2} (x y)}{{(z^{3})}^{2} \cdot 1}}$

Step 2.3

Rearrange the fraction $\frac{{(2 x y^{3})}^{2} (x y)}{{(z^{3})}^{2} \cdot 1}$ .

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

Step 3

Pull terms out from under the radical.

$\frac{2 x y^{3}}{z^{3}} \sqrt{x y}$

Step 4

Combine $\frac{2 x y^{3}}{z^{3}}$ and $\sqrt{x y}$ .

$\frac{2 x y^{3} \sqrt{x y}}{z^{3}}$