Basic Math Examples

$\sqrt{10 r^{2}} \cdot \sqrt{15 r^{3}}$

Step 1

Reorder $10$ and $r^{2}$ .

$\sqrt{r^{2} \cdot 10} \cdot \sqrt{15 r^{3}}$

Step 2

Pull terms out from under the radical.

$r \sqrt{10} \cdot \sqrt{15 r^{3}}$

Step 3

Rewrite $15 r^{3}$ as $r^{2} \cdot (15 r)$ .

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Step 3.1

Factor out $r^{2}$ .

$r \sqrt{10} \cdot \sqrt{15 (r^{2} r)}$

Step 3.2

Reorder $15$ and $r^{2}$ .

$r \sqrt{10} \cdot \sqrt{r^{2} \cdot 15 r}$

Step 3.3

Add parentheses.

$r \sqrt{10} \cdot \sqrt{r^{2} \cdot (15 r)}$

$r \sqrt{10} \cdot \sqrt{r^{2} \cdot (15 r)}$

Step 4

Pull terms out from under the radical.

$r \sqrt{10} \cdot (r \sqrt{15 r})$

Step 5

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

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Step 5.1

Move $r$ .

$r \cdot r \sqrt{10} \cdot \sqrt{15 r}$

Step 5.2

Multiply $r$ by $r$ .

$r^{2} \sqrt{10} \cdot \sqrt{15 r}$

$r^{2} \sqrt{10} \cdot \sqrt{15 r}$

Step 6

Multiply $r^{2} \sqrt{10} \sqrt{15 r}$ .

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Step 6.1

Combine using the product rule for radicals.

$r^{2} \sqrt{15 r \cdot 10}$

Step 6.2

Multiply $10$ by $15$ .

$r^{2} \sqrt{150 r}$

$r^{2} \sqrt{150 r}$

Step 7

Rewrite $150 r$ as $5^{2} \cdot (6 r)$ .

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Step 7.1

Factor $25$ out of $150$ .

$r^{2} \sqrt{25 (6) r}$

Step 7.2

Rewrite $25$ as $5^{2}$ .

$r^{2} \sqrt{5^{2} \cdot 6 r}$

Step 7.3

Add parentheses.

$r^{2} \sqrt{5^{2} \cdot (6 r)}$

$r^{2} \sqrt{5^{2} \cdot (6 r)}$

Step 8

Pull terms out from under the radical.

$r^{2} (5 \sqrt{6 r})$

Step 9

Rewrite using the commutative property of multiplication.

$5 r^{2} \sqrt{6 r}$

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