Question 130461
The problem states to rationalize the denominator. 

{{{sqrt(2 - 4/z^2 + 2/z^4)}}} 

I came up with {{{(z^2 - 1)sqrt(2)/z^2}}} 
Any help would be greatly appreciated. Thanks!

<pre><font size = 4><b>

Let's see:

{{{sqrt(2 - 4/z^2 + 2/z^4)}}}

{{{sqrt(2z^4/z^4 - (4z^2)/(z^2z^2) + 2/z^4)}}}

{{{sqrt(2z^4/z^4 - (4z^2)/z^4 + 2/z^4)}}}

{{{sqrt((2z^4 - 4z^2 + 2)/z^4)}}}

{{{sqrt(2z^4 - 4z^2 + 2)/sqrt(z^4)}}}

{{{sqrt(2(z^4 - 2z^2 + 1))/z^2}}}

{{{sqrt(2(z^2 - 1)(z^2 - 1))/z^2}}}
 
{{{sqrt(2(z^2 - 1)^2)/z^2}}}

{{{(sqrt(2)sqrt((z^2 - 1)^2))/z^2}}}

{{{(  sqrt(2)abs(z^2 - 1)   )/z^2}}}

Your answer is equivalent to mine, except for the 
absolute value bars.  The absolute value bars
are technically necessary because {{{z^2-1}}} 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</pre>