Algebra Examples

$2 \sqrt{50 a b^{5}}$

Step 1

Rewrite $50 a b^{5}$ as ${(5 b^{2})}^{2} \cdot (2 a b)$ .

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Step 1.1

Factor $25$ out of $50$ .

$2 \sqrt{25 (2) a b^{5}}$

Step 1.2

Rewrite $25$ as $5^{2}$ .

$2 \sqrt{5^{2} \cdot 2 a b^{5}}$

Step 1.3

Factor out $b^{4}$ .

$2 \sqrt{5^{2} \cdot 2 a (b^{4} b)}$

Step 1.4

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

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

Step 1.5

Move $a$ .

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

Step 1.6

Move $2$ .

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

Step 1.7

Rewrite $5^{2} {(b^{2})}^{2}$ as ${(5 b^{2})}^{2}$ .

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

Step 1.8

Add parentheses.

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

Step 1.9

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$2 (| 5 b^{2} | \sqrt{2 a b})$

Step 3

Remove non-negative terms from the absolute value.

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

Step 4

Multiply $5$ by $2$ .

$10 b^{2} \sqrt{2 a b}$