Basic Math Examples

$\sqrt{2 r^{3}} \cdot \sqrt{6 r^{2}}$

Step 1

Rewrite $2 r^{3}$ as $r^{2} \cdot (2 r)$ .

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Step 1.1

Factor out $r^{2}$ .

$\sqrt{2 (r^{2} r)} \cdot \sqrt{6 r^{2}}$

Step 1.2

Reorder $2$ and $r^{2}$ .

$\sqrt{r^{2} \cdot 2 r} \cdot \sqrt{6 r^{2}}$

Step 1.3

Add parentheses.

$\sqrt{r^{2} \cdot (2 r)} \cdot \sqrt{6 r^{2}}$

$\sqrt{r^{2} \cdot (2 r)} \cdot \sqrt{6 r^{2}}$

Step 2

Pull terms out from under the radical.

$r \sqrt{2 r} \cdot \sqrt{6 r^{2}}$

Step 3

Reorder $6$ and $r^{2}$ .

$r \sqrt{2 r} \cdot \sqrt{r^{2} \cdot 6}$

Step 4

Pull terms out from under the radical.

$r \sqrt{2 r} \cdot (r \sqrt{6})$

Step 5

Rewrite using the commutative property of multiplication.

$\sqrt{6} r \sqrt{2 r} r$

Step 6

Multiply $r$ by $r$ by adding the exponents.

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Step 6.1

Move $r$ .

$\sqrt{6} (r \cdot r) \sqrt{2 r}$

Step 6.2

Multiply $r$ by $r$ .

$\sqrt{6} r^{2} \sqrt{2 r}$

$\sqrt{6} r^{2} \sqrt{2 r}$

Step 7

Multiply $\sqrt{6} r^{2} \sqrt{2 r}$ .

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Step 7.1

Combine using the product rule for radicals.

$r^{2} \sqrt{6 (2 r)}$

Step 7.2

Multiply $6$ by $2$ .

$r^{2} \sqrt{12 r}$

$r^{2} \sqrt{12 r}$

Step 8

Rewrite $12 r$ as $2^{2} \cdot (3 r)$ .

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Step 8.1

Factor $4$ out of $12$ .

$r^{2} \sqrt{4 (3) r}$

Step 8.2

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

$r^{2} \sqrt{2^{2} \cdot 3 r}$

Step 8.3

Add parentheses.

$r^{2} \sqrt{2^{2} \cdot (3 r)}$

$r^{2} \sqrt{2^{2} \cdot (3 r)}$

Step 9

Pull terms out from under the radical.

$r^{2} (2 \sqrt{3 r})$

Step 10

Rewrite using the commutative property of multiplication.

$2 r^{2} \sqrt{3 r}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$