# Rationalizing the denominator and expressing a fraction as a surd

• Sep 9th 2007, 09:00 AM
Coach
Rationalizing the denominator and expressing a fraction as a surd
I'm sorry about the stupid questions, I just don't understand this.

Express these in surd form and rationalize the denominators

a)
$\displaystyle \frac{1}{1+cos45}$

Thank you so much!
• Sep 9th 2007, 09:05 AM
Jhevon
Quote:

Originally Posted by Coach
I'm sorry about the stupid questions, I just don't understand this.

express these in surd form and rationalize the denominators

a)
$\displaystyle \frac{1}{1+cos45}$

you should know that $\displaystyle \cos 45^{\circ} = \frac {\sqrt {2}}{2}$

so, $\displaystyle \frac {1}{1 + \cos 45} = \frac {1}{1 + \frac {\sqrt {2}}{2}}$

$\displaystyle = \frac {1}{\frac {2 + \sqrt {2}}{2}}$

$\displaystyle = \frac {2}{2 + \sqrt {2}}$

Now we need to rationalize this. I don't want to do all the work for you, so i'll tell you what to do.

multiply by the conjugate of the base ($\displaystyle 2 - \sqrt {2}$) over itself, and simplify