Algebra Examples

$\sqrt{20 e^{8 x}}$

Step 1

Rewrite $20 e^{8 x}$ as ${(2 e^{4 x})}^{2} \cdot 5$ .

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Step 1.1

Factor $4$ out of $20$ .

$\sqrt{4 (5) e^{8 x}}$

Step 1.2

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

$\sqrt{2^{2} \cdot 5 e^{8 x}}$

Step 1.3

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

$\sqrt{2^{2} \cdot 5 {(e^{4 x})}^{2}}$

Step 1.4

Move $5$ .

$\sqrt{2^{2} {(e^{4 x})}^{2} \cdot 5}$

Step 1.5

Rewrite $2^{2} {(e^{4 x})}^{2}$ as ${(2 e^{4 x})}^{2}$ .

$\sqrt{{(2 e^{4 x})}^{2} \cdot 5}$

Step 2

Pull terms out from under the radical.

$2 e^{4 x} \sqrt{5}$