Algebra Examples

$- x \sqrt{24} + 10 \sqrt{6 x^{2}}$

Step 1

Rewrite $24$ as $2^{2} \cdot 6$ .

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Step 1.1

Factor $4$ out of $24$ .

$- x \sqrt{4 (6)} + 10 \sqrt{6 x^{2}}$

Step 1.2

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

$- x \sqrt{2^{2} \cdot 6} + 10 \sqrt{6 x^{2}}$

Step 2

Pull terms out from under the radical.

$- x (| 2 | \sqrt{6}) + 10 \sqrt{6 x^{2}}$

Step 3

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$- x (2 \sqrt{6}) + 10 \sqrt{6 x^{2}}$

Step 4

Multiply $2$ by $- 1$ .

$- 2 x \sqrt{6} + 10 \sqrt{6 x^{2}}$

Step 5

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

$- 2 x \sqrt{6} + 10 \sqrt{x^{2} \cdot 6}$

Step 6

Pull terms out from under the radical.

$- 2 x \sqrt{6} + 10 | x | \sqrt{6}$