Algebra Examples

$\sqrt{81 a^{7} b^{12} c^{9}}$

Step 1

Rewrite $81 a^{7} b^{12} c^{9}$ as ${(9 a^{3} b^{6} c^{4})}^{2} (a c)$ .

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Step 1.1

Rewrite $81$ as $9^{2}$ .

$\sqrt{9^{2} a^{7} b^{12} c^{9}}$

Step 1.2

Factor out $a^{6}$ .

$\sqrt{9^{2} (a^{6} a) b^{12} c^{9}}$

Step 1.3

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

$\sqrt{9^{2} ({(a^{3})}^{2} a) b^{12} c^{9}}$

Step 1.4

Rewrite $b^{12}$ as ${(b^{6})}^{2}$ .

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

Step 1.5

Factor out $c^{8}$ .

$\sqrt{9^{2} ({(a^{3})}^{2} a) {(b^{6})}^{2} (c^{8} c)}$

Step 1.6

Rewrite $c^{8}$ as ${(c^{4})}^{2}$ .

$\sqrt{9^{2} ({(a^{3})}^{2} a) {(b^{6})}^{2} ({(c^{4})}^{2} c)}$

Step 1.7

Move $a$ .

$\sqrt{9^{2} ({(a^{3})}^{2}) {(b^{6})}^{2} {(c^{4})}^{2} a c}$

Step 1.8

Rewrite $9^{2} ({(a^{3})}^{2}) {(b^{6})}^{2} {(c^{4})}^{2}$ as ${(9 a^{3} b^{6} c^{4})}^{2}$ .

$\sqrt{{(9 a^{3} b^{6} c^{4})}^{2} a c}$

Step 1.9

Add parentheses.

$\sqrt{{(9 a^{3} b^{6} c^{4})}^{2} (a c)}$

Step 2

Pull terms out from under the radical.

$| 9 a^{3} b^{6} c^{4} | \sqrt{a c}$

Step 3

Remove non-negative terms from the absolute value.

$9 b^{6} c^{4} | a^{3} | \sqrt{a c}$