Algebra Examples

$\sqrt{\frac{5 x}{49 y^{4}}}$

Step 1

Rewrite $\frac{5 x}{49 y^{4}}$ as ${(\frac{1}{7 y^{2}})}^{2} (5 x)$ .

Tap for more steps...

Step 1.1

Factor the perfect power $1^{2}$ out of $5 x$ .

$\sqrt{\frac{1^{2} (5 x)}{49 y^{4}}}$

Step 1.2

Factor the perfect power ${(7 y^{2})}^{2}$ out of $49 y^{4}$ .

$\sqrt{\frac{1^{2} (5 x)}{{(7 y^{2})}^{2} \cdot 1}}$

Step 1.3

Rearrange the fraction $\frac{1^{2} (5 x)}{{(7 y^{2})}^{2} \cdot 1}$ .

$\sqrt{{(\frac{1}{7 y^{2}})}^{2} (5 x)}$

Step 2

Pull terms out from under the radical.

$| \frac{1}{7 y^{2}} | \sqrt{5 x}$

Step 3

Remove non-negative terms from the absolute value.

$\frac{| 1 |}{7 y^{2}} \sqrt{5 x}$

Step 4

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

$\frac{1}{7 y^{2}} \sqrt{5 x}$

Step 5

Combine $\frac{1}{7 y^{2}}$ and $\sqrt{5 x}$ .

$\frac{\sqrt{5 x}}{7 y^{2}}$