Basic Math Examples

$\sqrt{2 r} \cdot (- 2 \sqrt{8 r^{2}})$

Step 1

Rewrite using the commutative property of multiplication.

$- 2 \sqrt{2 r} \sqrt{8 r^{2}}$

Step 2

Rewrite $8 r^{2}$ as ${(2 r)}^{2} \cdot 2$ .

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Step 2.1

Factor $4$ out of $8$ .

$- 2 \sqrt{2 r} \sqrt{4 (2) r^{2}}$

Step 2.2

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

$- 2 \sqrt{2 r} \sqrt{2^{2} \cdot 2 r^{2}}$

Step 2.3

Move $2$ .

$- 2 \sqrt{2 r} \sqrt{2^{2} r^{2} \cdot 2}$

Step 2.4

Rewrite $2^{2} r^{2}$ as ${(2 r)}^{2}$ .

$- 2 \sqrt{2 r} \sqrt{{(2 r)}^{2} \cdot 2}$

Step 3

Pull terms out from under the radical.

$- 2 \sqrt{2 r} (2 r \sqrt{2})$

Step 4

Multiply $- 2 \sqrt{2 r} (2 r \sqrt{2})$ .

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Step 4.1

Multiply $2$ by $- 2$ .

$- 4 \sqrt{2 r} (r \sqrt{2})$

Step 4.2

Combine using the product rule for radicals.

$- 4 (r \sqrt{2 r \cdot 2})$

Step 4.3

Multiply $2$ by $2$ .

$- 4 (r \sqrt{4 r})$

Step 5

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

$- 4 (r \sqrt{2^{2} r})$

Step 6

Pull terms out from under the radical.

$- 4 (r (2 \sqrt{r}))$

Step 7

Simplify the expression.

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Step 7.1

Rewrite using the commutative property of multiplication.

$- 4 (2 r \sqrt{r})$

Step 7.2

Multiply $2$ by $- 4$ .

$- 8 r \sqrt{r}$