Algebra Examples

$\sqrt{12 m} \cdot \sqrt{15 m}$

Step 1

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

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Step 1.1

Factor $4$ out of $12$ .

$\sqrt{4 (3) m} \cdot \sqrt{15 m}$

Step 1.2

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

$\sqrt{2^{2} \cdot 3 m} \cdot \sqrt{15 m}$

Step 1.3

Add parentheses.

$\sqrt{2^{2} \cdot (3 m)} \cdot \sqrt{15 m}$

$\sqrt{2^{2} \cdot (3 m)} \cdot \sqrt{15 m}$

Step 2

Pull terms out from under the radical.

$2 \sqrt{3 m} \cdot \sqrt{15 m}$

Step 3

Multiply $2 \sqrt{3 m} \sqrt{15 m}$ .

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Step 3.1

Combine using the product rule for radicals.

$2 \sqrt{15 m (3 m)}$

Step 3.2

Multiply $3$ by $15$ .

$2 \sqrt{45 m \cdot m}$

Step 3.3

Raise $m$ to the power of $1$ .

$2 \sqrt{45 (m^{1} m)}$

Step 3.4

Raise $m$ to the power of $1$ .

$2 \sqrt{45 (m^{1} m^{1})}$

Step 3.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \sqrt{45 m^{1 + 1}}$

Step 3.6

Add $1$ and $1$ .

$2 \sqrt{45 m^{2}}$

$2 \sqrt{45 m^{2}}$

Step 4

Rewrite $45 m^{2}$ as ${(3 m)}^{2} \cdot 5$ .

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Step 4.1

Factor $9$ out of $45$ .

$2 \sqrt{9 (5) m^{2}}$

Step 4.2

Rewrite $9$ as $3^{2}$ .

$2 \sqrt{3^{2} \cdot 5 m^{2}}$

Step 4.3

Move $5$ .

$2 \sqrt{3^{2} m^{2} \cdot 5}$

Step 4.4

Rewrite $3^{2} m^{2}$ as ${(3 m)}^{2}$ .

$2 \sqrt{{(3 m)}^{2} \cdot 5}$

$2 \sqrt{{(3 m)}^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$2 (3 m \sqrt{5})$

Step 6

Multiply $3$ by $2$ .

$6 m \sqrt{5}$

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