skip to main content
this is a free sample lesson. sign up for magoosh to get access to over 200 video lessons.

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.