Algebra Examples

$\sqrt{32 x^{5}}$

Step 1

Rewrite $32 x^{5}$ as ${(4 x^{2})}^{2} \cdot (2 x)$ .

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Step 1.1

Factor $16$ out of $32$ .

$\sqrt{16 (2) x^{5}}$

Step 1.2

Rewrite $16$ as $4^{2}$ .

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

Step 1.3

Factor out $x^{4}$ .

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

Step 1.4

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

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

Step 1.5

Move $2$ .

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

Step 1.6

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

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

Step 1.7

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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