Surds: Rationalizing the Denominator

In this video, I demonstrate how to rationalize the denominator of a fractional surd with a rule / technique learned in basic algebra called "the difference of 2 squares" - which is the result of multiplication by the conjugate.

We start with the fraction:

\frac{1}{2\sqrt5-\sqrt3}

Now, the difference of 2 squares a² - b² can be expressed as (a-b)(a+b). So if you apply the same principle here and multiply the denominator by 2√5 + √3, we can turn it into an integer.

However, since we multiply the denominator by 2√5 + √3, we also need to multiply the numerator by this as well, so that we are effectively multiplying the entire expression by 1.

Hence:

\frac{1}{2\sqrt5-\sqrt3}=\frac{1}{2\sqrt5-\sqrt3}\times \frac{2\sqrt5+\sqrt3}{2\sqrt5+\sqrt3}

Thanks for watching. Please give me a "thumbs up" if you have found this video helpful.

Please ask me a maths question by commenting below and I will try to help you in future videos.