Rational? Real!

Algebra Level 2

If $y=\sqrt{x^{3}}$ , what values of $y$ will make $\dfrac{1}{\sqrt{x-1}}$ real?

All real numbers

y<-1

y<2

y>1

y>3

1 solution

Margaret Zheng
Feb 7, 2016

For $\frac{1}{\sqrt{x-1}}$ to be real, $x$ must be greater than 1. That makes $x^{3}$ and its square root greater than 1; therefore, our answer is $y>1$ .

Moderator note:

Simple standard approach.

There is a typo. You meant $\frac{1}{ \sqrt{x-1}}$ instead of just $\frac{1}{ x-1 }$ .

Calvin Lin Staff - 5 years, 3 months ago

Thank you and does it seem correct now?

Margaret Zheng - 5 years, 3 months ago

It's great now :)

Calvin Lin Staff - 5 years, 3 months ago

Rational? Real!

1 solution

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