SOLUTION: The problem states to rationalize the denominator. The sqrt of 2 - 4/z^2 + 2/z^4 I came up with (z^2 - 1) * sqrt of 2 over z^2 Any help would be greatly appreciated. Tha

Algebra ->  Radicals -> SOLUTION: The problem states to rationalize the denominator. The sqrt of 2 - 4/z^2 + 2/z^4 I came up with (z^2 - 1) * sqrt of 2 over z^2 Any help would be greatly appreciated. Tha      Log On


   

Question 130461This question is from textbook Introductory Algebra
: The problem states to rationalize the denominator.
The sqrt of 2 - 4/z^2 + 2/z^4
I came up with (z^2 - 1) * sqrt of 2 over z^2
Any help would be greatly appreciated. Thanks! This question is from textbook Introductory Algebra

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The problem states to rationalize the denominator.
sqrt%282+-+4%2Fz%5E2+%2B+2%2Fz%5E4%29
I came up with %28z%5E2+-+1%29sqrt%282%29%2Fz%5E2
Any help would be greatly appreciated. Thanks! 


Let's see:

sqrt%282+-+4%2Fz%5E2+%2B+2%2Fz%5E4%29

sqrt%282z%5E4%2Fz%5E4+-+%284z%5E2%29%2F%28z%5E2z%5E2%29+%2B+2%2Fz%5E4%29

sqrt%282z%5E4%2Fz%5E4+-+%284z%5E2%29%2Fz%5E4+%2B+2%2Fz%5E4%29

sqrt%28%282z%5E4+-+4z%5E2+%2B+2%29%2Fz%5E4%29

sqrt%282z%5E4+-+4z%5E2+%2B+2%29%2Fsqrt%28z%5E4%29

sqrt%282%28z%5E4+-+2z%5E2+%2B+1%29%29%2Fz%5E2

sqrt%282%28z%5E2+-+1%29%28z%5E2+-+1%29%29%2Fz%5E2
 
sqrt%282%28z%5E2+-+1%29%5E2%29%2Fz%5E2

%28sqrt%282%29sqrt%28%28z%5E2+-+1%29%5E2%29%29%2Fz%5E2

%28++sqrt%282%29abs%28z%5E2+-+1%29+++%29%2Fz%5E2

Your answer is equivalent to mine, except for the 
absolute value bars.  The absolute value bars
are technically necessary because z%5E2-1 is
negative when z < 1, yet by agreement no radical 
square root can ever be negative.

However your teacher may just ignore this fact
and accept your answer as you have it without the 
absolute value bars.

Edwin