Question

Hi ya!
So I got a question like when I'm rationalzing a denomenator in order to get simple radical form I really don't know what to do

for example this problem

(6^(2^-1)-3^(2^-1))^-1

ok so I know your trying to get it so it's a perfect sqaure right so I can legally write this

(6^(2^-1)-3^(2^-1))^-1 A = (6 - 3)^-1 = 3^-1

or a simplified formula

(6^(2^-1)-3^(2^-1))^-1 A = 3^-1
and solve for A were A equals the value needed to get the perfect square 6-3 or simply 3 right so I solved

A=3^-1(6^(2^-1)-3^(2^-1))

and I get some value which is equal to
(6^(2^-1)+3^(2^-1))^-1
but where s the proof that this is correct using that formula all you get is some number and I have no idea how you get this answer I know you just make the negetive positive but what allows you to do that?????

Answer 1

You still haven't read about conjugates. You are NOT trying to get a perfect square, you are trying to get a difference of perfect squares.
http://www.regentsprep.org/Regents/math/algtrig/ATO3/rdlesson.htm