Algebra Examples

$- 3 \sqrt{24 a^{4} b^{2} c^{3}}$

Step 1

Rewrite $24 a^{4} b^{2} c^{3}$ as ${(2 a^{2} b c)}^{2} \cdot (6 c)$ .

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Step 1.1

Factor $4$ out of $24$ .

$- 3 \sqrt{4 (6) a^{4} b^{2} c^{3}}$

Step 1.2

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

$- 3 \sqrt{2^{2} \cdot 6 a^{4} b^{2} c^{3}}$

Step 1.3

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

$- 3 \sqrt{2^{2} \cdot 6 {(a^{2})}^{2} b^{2} c^{3}}$

Step 1.4

Factor out $c^{2}$ .

$- 3 \sqrt{2^{2} \cdot 6 {(a^{2})}^{2} b^{2} (c^{2} c)}$

Step 1.5

Move $6$ .

$- 3 \sqrt{2^{2} {(a^{2})}^{2} b^{2} c^{2} \cdot 6 c}$

Step 1.6

Rewrite $2^{2} {(a^{2})}^{2} b^{2} c^{2}$ as ${(2 a^{2} b c)}^{2}$ .

$- 3 \sqrt{{(2 a^{2} b c)}^{2} \cdot 6 c}$

Step 1.7

Add parentheses.

$- 3 \sqrt{{(2 a^{2} b c)}^{2} \cdot (6 c)}$

Step 2

Pull terms out from under the radical.

$- 3 (2 a^{2} b c \sqrt{6 c})$

Step 3

Multiply $2$ by $- 3$ .

$- 6 a^{2} b c \sqrt{6 c}$