Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Factor out $c^{2}$ .

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

Step 1.4

Move $b$ .

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

Step 1.5

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

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

Step 1.6

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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