How does sqrt(x^2) = 1?

**hydride** · March 13th 2011, 10:56 PM

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.

**Prove It** · March 13th 2011, 11:25 PM

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.

**hydride** · March 13th 2011, 11:46 PM

Thank you! I got it.

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