Finite Math Examples

$\sqrt{20 a^{4} b^{5}}$

Step 1

Rewrite $20 a^{4} b^{5}$ as ${(2 a^{2} b^{2})}^{2} \cdot (5 b)$ .

Tap for more steps...

Step 1.1

Factor $4$ out of $20$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Factor out $b^{4}$ .

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

Step 1.5

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

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

Step 1.6

Move $5$ .

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

Step 1.7

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

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

Step 1.8

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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