Question

A question asks determine the exact value of sin45 degrees. The sin45 = 1/root 2. Then you multiply that with root 2 over root 2 to get root 2 over 2. Why do you have to multiply by root 2 over root 2, to get the answer?

Answer 1

Its more of a preference than anything else really. Some people don't like seeing square roots in the denominator of fractions (I personally don't get what the big deal is about it), so we rationalize them by multiplying the numerator and denominator by the square root term in question.

In this instance, we rewrite \(\dfrac{1}{\sqrt{2}}\) by multiplying it by the fraction \(\dfrac{\sqrt{2}}{\sqrt{2}}\) to see that \(\dfrac{1}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{\sqrt{2}}{(\sqrt{2})^2} = \dfrac{\sqrt{2}}{2}\).

By the way, in the classes I teach, I don't require them to do this. XD

I hope this clarifies things! :-)

Answer 2

When it comes to adding fractions, it may be easier to do so with a rational denominator. So that may be one reason why a lot of books and teachers have you rationalize the denominator.

Answer 3

@jim_thompson5910 Ah yes, you have a point. XD

Answer 4

Thank you :)