Algebra Examples

$6 x \sqrt{3 x} - 6 \sqrt{48 x^{3}}$

Step 1

Rewrite $48 x^{3}$ as ${(4 x)}^{2} \cdot (3 x)$ .

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Step 1.1

Factor $16$ out of $48$ .

$6 x \sqrt{3 x} - 6 \sqrt{16 (3) x^{3}}$

Step 1.2

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

$6 x \sqrt{3 x} - 6 \sqrt{4^{2} \cdot 3 x^{3}}$

Step 1.3

Factor out $x^{2}$ .

$6 x \sqrt{3 x} - 6 \sqrt{4^{2} \cdot 3 (x^{2} x)}$

Step 1.4

Move $3$ .

$6 x \sqrt{3 x} - 6 \sqrt{4^{2} x^{2} \cdot 3 x}$

Step 1.5

Rewrite $4^{2} x^{2}$ as ${(4 x)}^{2}$ .

$6 x \sqrt{3 x} - 6 \sqrt{{(4 x)}^{2} \cdot 3 x}$

Step 1.6

Add parentheses.

$6 x \sqrt{3 x} - 6 \sqrt{{(4 x)}^{2} \cdot (3 x)}$

Step 2

Pull terms out from under the radical.

$6 x \sqrt{3 x} - 6 (| 4 x | \sqrt{3 x})$

Step 3

Remove non-negative terms from the absolute value.

$6 x \sqrt{3 x} - 6 (4 | x | \sqrt{3 x})$

Step 4

Multiply $4$ by $- 6$ .

$6 x \sqrt{3 x} - 24 | x | \sqrt{3 x}$