## X with a fraction as an exponent

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
drummergirl95
Posts: 1
Joined: Wed Apr 20, 2011 8:53 pm
Contact:

### X with a fraction as an exponent

This is my problem:
Simplify: 1/(X^1/2 + Y^1/2)
I know this should be easy, and I know that the X should go in a radical as well as the Y, but I don't fully understand the "simplify" part.... help??

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
Contact:

### Re: X with a fraction as an exponent

This is my problem:
Simplify: 1/(X^1/2 + Y^1/2)
I know this should be easy, and I know that the X should go in a radical as well as the Y, but I don't fully understand the "simplify" part.... help??
if you have $\frac{1}{x^{1/2}+y^{1/2}}=\frac{1}{\sqrt{x}+\sqrt{y}}$

then I don't think you can simplify it any further than it is already.

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
Simplify: 1/(X^1/2 + Y^1/2)
Are you maybe supposed to "rationalize" the denominator? If so, then multiply by the conjugate of the denominator:

. . . . .$\left(\frac{1}{\sqrt{x}\, +\, \sqrt{y}}\right)\left(\frac{\sqrt{x}\, -\, \sqrt{y}}{\sqrt{x}\, -\, \sqrt{y}}\right)$

The radical terms will cancel out in the denominator.