## X with a fraction as an exponent

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
drummergirl95
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### 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
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### Re: X with a fraction as an exponent

drummergirl95 wrote: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
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drummergirl95 wrote: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.