Finite Math Examples

$\sqrt{- \frac{r}{5}} \cdot \sqrt{- \frac{20}{r}}$

Step 1

Multiply $\sqrt{- \frac{r}{5}} \sqrt{- \frac{20}{r}}$ .

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Step 1.1

Combine using the product rule for radicals.

$\sqrt{- \frac{r}{5} (- \frac{20}{r})}$

Step 1.2

Multiply $- 1$ by $- 1$ .

$\sqrt{1 \frac{r}{5} \frac{20}{r}}$

Step 1.3

Multiply $\frac{r}{5}$ by $1$ .

$\sqrt{\frac{r}{5} \cdot \frac{20}{r}}$

Step 1.4

Multiply $\frac{r}{5}$ by $\frac{20}{r}$ .

$\sqrt{\frac{r \cdot 20}{5 r}}$

Step 2

Reduce the expression $\frac{r \cdot 20}{5 r}$ by cancelling the common factors.

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Step 2.1

Cancel the common factor.

$\sqrt{\frac{r \cdot 20}{5 r}}$

Step 2.2

Rewrite the expression.

$\sqrt{\frac{20}{5}}$

Step 3

Simplify the expression.

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Step 3.1

Divide $20$ by $5$ .

$\sqrt{4}$

Step 3.2

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

$\sqrt{2^{2}}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$2$