# Thread: How does sqrt(x^2) = 1?

1. ## How does sqrt(x^2) = 1?

Hey guys, I just have quick question:

How does $\frac{\sqrt{9x^2+x}}{x} = \sqrt{9+1/x}$ knowing that $\sqrt{x^2} = x$

big thanks.

2. Assuming that $\displaystyle x \geq 0$, then $\displaystyle \sqrt{x^2} = x$.

Since $\displaystyle \frac{\sqrt{9x^2 + x}}{x} = \frac{\sqrt{9x^2 + x}}{\sqrt{x^2}}$

$\displaystyle = \sqrt{\frac{9x^2 + x}{x^2}}$.

Go from here.

3. Thank you! I got it.