## Rationalizing

Summary

The content focuses on the concept of rationalizing denominators in mathematical expressions, particularly those involving radicals, as a crucial skill for GRE exam preparation.

- Rationalizing is the process of eliminating radicals from the denominator of a fraction to adhere to mathematical conventions and ease the comparison of answers.
- For single radicals in the denominator, rationalization involves multiplying the fraction by the radical over itself.
- When the denominator contains addition or subtraction involving radicals, rationalization requires multiplying by the conjugate of the denominator.
- Practical examples and exercises are provided to demonstrate the process of rationalizing different types of fractions.
- Understanding and applying the concept of rationalizing is essential for matching answers to the rationalized form presented in GRE test options.

Chapters

00:01

Introduction to Rationalizing

01:46

Rationalizing Single Radicals

04:44

Rationalizing with Addition or Subtraction

08:07

Applying the Conjugate Method

13:14

Summary of Rationalizing Process

**Q: Around ~11:45, how do we simplify (2+2√5)/4 into (1+√5)/2?**

**A: **Great question! We can factor out a 2 from the numerator: (**2**+**2**√5) --> **2**(1+√5).

Now, if we put the numerator and denominator back together, we'll see that we can divide both by 2: **2**(1+√5)/**4** = (1+√5)/2.

Since there isn't another factor of 2 in the numerator, we can't simplify further. So, our final answer (1+√5)/2.