Rationalizing
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Powers and Roots
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.