Algebra Examples

$(- \sqrt{8 m}) (\sqrt{6 m})$

Step 1

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

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Step 1.1

Factor $4$ out of $8$ .

$- \sqrt{4 (2) m} \sqrt{6 m}$

Step 1.2

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

$- \sqrt{2^{2} \cdot 2 m} \sqrt{6 m}$

Step 1.3

Add parentheses.

$- \sqrt{2^{2} \cdot (2 m)} \sqrt{6 m}$

$- \sqrt{2^{2} \cdot (2 m)} \sqrt{6 m}$

Step 2

Pull terms out from under the radical.

$- (2 \sqrt{2 m}) \sqrt{6 m}$

Step 3

Multiply $2$ by $- 1$ .

$- 2 \sqrt{2 m} \sqrt{6 m}$

Step 4

Multiply $- 2 \sqrt{2 m} \sqrt{6 m}$ .

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Step 4.1

Combine using the product rule for radicals.

$- 2 \sqrt{6 m (2 m)}$

Step 4.2

Multiply $2$ by $6$ .

$- 2 \sqrt{12 m \cdot m}$

Step 4.3

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

$- 2 \sqrt{12 (m^{1} m)}$

Step 4.4

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

$- 2 \sqrt{12 (m^{1} m^{1})}$

Step 4.5

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

$- 2 \sqrt{12 m^{1 + 1}}$

Step 4.6

Add $1$ and $1$ .

$- 2 \sqrt{12 m^{2}}$

$- 2 \sqrt{12 m^{2}}$

Step 5

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

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Step 5.1

Factor $4$ out of $12$ .

$- 2 \sqrt{4 (3) m^{2}}$

Step 5.2

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

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

Step 5.3

Move $3$ .

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

Step 5.4

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

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

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

Step 6

Pull terms out from under the radical.

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

Step 7

Multiply $2$ by $- 2$ .

$- 4 m \sqrt{3}$

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