Algebra Examples

$\sqrt{600 a^{9} b^{7} c^{11}}$

Step 1

Rewrite $600 a^{9} b^{7} c^{11}$ as ${(10 a^{4} b^{3} c^{5})}^{2} \cdot (6 a b c)$ .

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Step 1.1

Factor $100$ out of $600$ .

$\sqrt{100 (6) a^{9} b^{7} c^{11}}$

Step 1.2

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} \cdot 6 a^{9} b^{7} c^{11}}$

Step 1.3

Factor out $a^{8}$ .

$\sqrt{10^{2} \cdot 6 (a^{8} a) b^{7} c^{11}}$

Step 1.4

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

$\sqrt{10^{2} \cdot 6 ({(a^{4})}^{2} a) b^{7} c^{11}}$

Step 1.5

Factor out $b^{6}$ .

$\sqrt{10^{2} \cdot 6 ({(a^{4})}^{2} a) (b^{6} b) c^{11}}$

Step 1.6

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

$\sqrt{10^{2} \cdot 6 ({(a^{4})}^{2} a) ({(b^{3})}^{2} b) c^{11}}$

Step 1.7

Factor out $c^{10}$ .

$\sqrt{10^{2} \cdot 6 ({(a^{4})}^{2} a) ({(b^{3})}^{2} b) (c^{10} c)}$

Step 1.8

Rewrite $c^{10}$ as ${(c^{5})}^{2}$ .

$\sqrt{10^{2} \cdot 6 ({(a^{4})}^{2} a) ({(b^{3})}^{2} b) ({(c^{5})}^{2} c)}$

Step 1.9

Move $b$ .

$\sqrt{10^{2} \cdot 6 ({(a^{4})}^{2} a) ({(b^{3})}^{2}) {(c^{5})}^{2} b c}$

Step 1.10

Move $a$ .

$\sqrt{10^{2} \cdot 6 ({(a^{4})}^{2}) ({(b^{3})}^{2}) {(c^{5})}^{2} a b c}$

Step 1.11

Move $6$ .

$\sqrt{(10^{2} ({(a^{4})}^{2})) ({(b^{3})}^{2}) {(c^{5})}^{2} \cdot 6 a b c}$

Step 1.12

Rewrite $((10^{2} ({(a^{4})}^{2})) ({(b^{3})}^{2})) {(c^{5})}^{2}$ as ${(10 a^{4} b^{3} c^{5})}^{2}$ .

$\sqrt{{(10 a^{4} b^{3} c^{5})}^{2} \cdot 6 a b c}$

Step 1.13

Add parentheses.

$\sqrt{{(10 a^{4} b^{3} c^{5})}^{2} \cdot 6 a (b c)}$

Step 1.14

Add parentheses.

$\sqrt{{(10 a^{4} b^{3} c^{5})}^{2} \cdot 6 (a (b c))}$

Step 1.15

Add parentheses.

$\sqrt{{(10 a^{4} b^{3} c^{5})}^{2} \cdot (6 a b c)}$

Step 2

Pull terms out from under the radical.

$10 a^{4} b^{3} c^{5} \sqrt{6 a b c}$