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.