Algebra Examples

$- \sqrt{6 x^{2}} + 8 x \sqrt{96}$

Step 1

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

$- \sqrt{x^{2} \cdot 6} + 8 x \sqrt{96}$

Step 2

Pull terms out from under the radical.

$- (| x | \sqrt{6}) + 8 x \sqrt{96}$

Step 3

Rewrite $96$ as $4^{2} \cdot 6$ .

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Step 3.1

Factor $16$ out of $96$ .

$- | x | \sqrt{6} + 8 x \sqrt{16 (6)}$

Step 3.2

Rewrite $16$ as $4^{2}$ .

$- | x | \sqrt{6} + 8 x \sqrt{4^{2} \cdot 6}$

Step 4

Pull terms out from under the radical.

$- | x | \sqrt{6} + 8 x (| 4 | \sqrt{6})$

Step 5

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$- | x | \sqrt{6} + 8 x (4 \sqrt{6})$

Step 6

Multiply $4$ by $8$ .

$- | x | \sqrt{6} + 32 x \sqrt{6}$