Algebra Examples

$\sqrt{18 a^{6} b^{3} c^{5}}$

Step 1

Rewrite $18 a^{6} b^{3} c^{5}$ as ${(3 a^{3} b c^{2})}^{2} \cdot (2 b c)$ .

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Step 1.1

Factor $9$ out of $18$ .

$\sqrt{9 (2) a^{6} b^{3} c^{5}}$

Step 1.2

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 2 a^{6} b^{3} c^{5}}$

Step 1.3

Rewrite $a^{6}$ as ${(a^{3})}^{2}$ .

$\sqrt{3^{2} \cdot 2 {(a^{3})}^{2} b^{3} c^{5}}$

Step 1.4

Factor out $b^{2}$ .

$\sqrt{3^{2} \cdot 2 {(a^{3})}^{2} (b^{2} b) c^{5}}$

Step 1.5

Factor out $c^{4}$ .

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

Step 1.6

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

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

Step 1.7

Move $b$ .

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

Step 1.8

Move $2$ .

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

Step 1.9

Rewrite $(3^{2} {(a^{3})}^{2} (b^{2})) {(c^{2})}^{2}$ as ${(3 a^{3} b c^{2})}^{2}$ .

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

Step 1.10

Add parentheses.

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

Step 1.11

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$| 3 a^{3} b c^{2} | \sqrt{2 b c}$

Step 3

Remove non-negative terms from the absolute value.

$3 c^{2} | a^{3} b | \sqrt{2 b c}$