Algebra Examples

$\sqrt{\frac{80 w^{3}}{9}}$

Step 1

Rewrite $\frac{80 w^{3}}{9}$ as ${(\frac{4 w}{3})}^{2} (5 w)$ .

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Step 1.1

Factor the perfect power ${(4 w)}^{2}$ out of $80 w^{3}$ .

$\sqrt{\frac{{(4 w)}^{2} \cdot (5 w)}{9}}$

Step 1.2

Factor the perfect power $3^{2}$ out of $9$ .

$\sqrt{\frac{{(4 w)}^{2} \cdot (5 w)}{3^{2} \cdot 1}}$

Step 1.3

Rearrange the fraction $\frac{{(4 w)}^{2} \cdot (5 w)}{3^{2} \cdot 1}$ .

$\sqrt{{(\frac{4 w}{3})}^{2} (5 w)}$

Step 2

Pull terms out from under the radical.

$\frac{4 w}{3} \sqrt{5 w}$

Step 3

Combine $\frac{4 w}{3}$ and $\sqrt{5 w}$ .

$\frac{4 w \sqrt{5 w}}{3}$