Greetings everyone,
I have got to simplify this very long expression. For the sake of simplicity, I'm not going to post it all. This is the last point up to which I am sure everything is correct:
From here it is not hard to get the 2 big square roots, then just multiply and at last the top and the bottom parts pretty much just simplify out, leaving the answer of 1/sqrt(a). Or so I thought.
The answer given in the book is this: 1/sqrt(a) when sqrt(2a) > 5b^(1/3) or 1/-sqrt(a) if otherwise.
If I understand correctly, what one should do is replace the approporiate part of the expression with this. Right?
What I absolutely can't understand is why isn't the same done with the a+sqrt(b) part (the first thing in the numerator). Why do we disregard the fact that it is also exactly the same - an expression raised to the power of 2 and square rooted? Is there some reason why a+sqrt(b) is always positive?
Every person I have tried to ask did not understand what I mean, so I'm starting to think this is a stupid question. Or maybe I am just asking in a way that's too complicated. If either is true, I am really sorry! I can try to make my question more clear, just ask!
I have got to simplify this very long expression. For the sake of simplicity, I'm not going to post it all. This is the last point up to which I am sure everything is correct:
From here it is not hard to get the 2 big square roots, then just multiply and at last the top and the bottom parts pretty much just simplify out, leaving the answer of 1/sqrt(a). Or so I thought.
The answer given in the book is this: 1/sqrt(a) when sqrt(2a) > 5b^(1/3) or 1/-sqrt(a) if otherwise.
If I understand correctly, what one should do is replace the approporiate part of the expression with this. Right?
What I absolutely can't understand is why isn't the same done with the a+sqrt(b) part (the first thing in the numerator). Why do we disregard the fact that it is also exactly the same - an expression raised to the power of 2 and square rooted? Is there some reason why a+sqrt(b) is always positive?
Every person I have tried to ask did not understand what I mean, so I'm starting to think this is a stupid question. Or maybe I am just asking in a way that's too complicated. If either is true, I am really sorry! I can try to make my question more clear, just ask!