Pre-Algebra Examples

$2 a \sqrt{44 a^{3} b^{7} c^{9}}$

Step 1

Rewrite $44 a^{3} b^{7} c^{9}$ as ${(2 a b^{3} c^{4})}^{2} \cdot (11 a b c)$ .

Tap for more steps...

Step 1.1

Factor $4$ out of $44$ .

$2 a \sqrt{4 (11) a^{3} b^{7} c^{9}}$

Step 1.2

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

$2 a \sqrt{2^{2} \cdot 11 a^{3} b^{7} c^{9}}$

Step 1.3

Factor out $a^{2}$ .

$2 a \sqrt{2^{2} \cdot 11 (a^{2} a) b^{7} c^{9}}$

Step 1.4

Factor out $b^{6}$ .

$2 a \sqrt{2^{2} \cdot 11 (a^{2} a) (b^{6} b) c^{9}}$

Step 1.5

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

$2 a \sqrt{2^{2} \cdot 11 (a^{2} a) ({(b^{3})}^{2} b) c^{9}}$

Step 1.6

Factor out $c^{8}$ .

$2 a \sqrt{2^{2} \cdot 11 (a^{2} a) ({(b^{3})}^{2} b) (c^{8} c)}$

Step 1.7

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

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

Step 1.8

Move $b$ .

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

Step 1.9

Move $a$ .

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

Step 1.10

Move $11$ .

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

Step 1.11

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

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

Step 1.12

Add parentheses.

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

Step 1.13

Add parentheses.

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

Step 1.14

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $a$ by $a$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $a$ .

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

Step 3.2

Multiply $a$ by $a$ .

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

Step 4

Multiply $2$ by $2$ .

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

Step 5

Reorder factors in $4 a^{2} (b^{3} c^{4} \sqrt{11 a b c})$ .

$4 a^{2} b^{3} c^{4} \sqrt{11 a b c}$