Algebra Examples

$\sqrt{\frac{33}{x^{4}}}$

Step 1

Rewrite $\frac{33}{x^{4}}$ as ${(\frac{1}{x^{2}})}^{2} \cdot 33$ .

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Step 1.1

Factor the perfect power $1^{2}$ out of $33$ .

$\sqrt{\frac{1^{2} \cdot 33}{x^{4}}}$

Step 1.2

Factor the perfect power ${(x^{2})}^{2}$ out of $x^{4}$ .

$\sqrt{\frac{1^{2} \cdot 33}{{(x^{2})}^{2} \cdot 1}}$

Step 1.3

Rearrange the fraction $\frac{1^{2} \cdot 33}{{(x^{2})}^{2} \cdot 1}$ .

$\sqrt{{(\frac{1}{x^{2}})}^{2} \cdot 33}$

Step 2

Pull terms out from under the radical.

$| \frac{1}{x^{2}} | \sqrt{33}$

Step 3

Remove non-negative terms from the absolute value.

$\frac{| 1 |}{x^{2}} \sqrt{33}$

Step 4

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{1}{x^{2}} \sqrt{33}$

Step 5

Combine $\frac{1}{x^{2}}$ and $\sqrt{33}$ .

$\frac{\sqrt{33}}{x^{2}}$