rationalize a denominator

[bobisaka]

in my understanding the denominator would become :


Than the fourth root would be: 2x

In the textbook example, in the second step in screenshot, how did they simplify without the radical:



And than how did they get x as their final answer?

 

[JeffM]

You are correct

[math]\sqrt[4]{2^4x^4} = 2x.[/math]
Whoever “they” may be, their second line is wrong.

Their third line, however, is correct. The factors of 2 in numerator and denominator cancel.

 

[pka]

[math]\sqrt[4]{2^4x^4} = 2x.[/math]

Actually it should be [imath]\sqrt[4]{2^4x^4} = 2\large{|x|}.[/imath]

 

[Steven G]

I 2nd pka's result. The simplification should be 2|x|.