# Math Help - Rationalizing the denominator and expressing a fraction as a surd

1. ## 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)
$\frac{1}{1+cos45}$

Thank you so much!

2. 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)
$\frac{1}{1+cos45}$
you should know that $\cos 45^{\circ} = \frac {\sqrt {2}}{2}$

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

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

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

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 ( $2 - \sqrt {2}$) over itself, and simplify