I3igDmsu wrote:

Can you use the FOIL method here? I guess what I am getting at is if you have an expression under a root and that expression is squared. Do you FOIL out the two expressions? How do you do it with roots?

You are not making fun of me, are you?

I will suppose that not and will respond. You mean put it this way \((\sqrt{n+1})(\sqrt{n+1})\)?

No you can't use FOIL because both terms are under one root. You could have used FOIL if it would have been \((\sqrt{n}+1)^2 =(\sqrt{n}+1)(\sqrt{n}+1)\) , but even in that case it would be more logical to use perfect square binomial identity - \((a+b)^2 = a^2+2ab+b^2\) (

Note: you really have to know basic polynomial identities. Make sure you know the answer to these - \((a \pm b)^2 = ? a^2-b^2=?\) and maybe \(a^3 \pm b^3=? (a \pm b)^3 =?\))

BUT in your case, as I said \((\sqrt{n+1})^2 = ((n+1)^{1/2})^2\) Note the brackets. You can't use FOIL because of the priority of the operations first you have too take the root (put to the 1/2 power) then square (multiply the brackets)....

To tickle your mind (or maybe to confuse you, so may disregard this part) I could abstractly show this in terms of a function of higher order... like \(f(x) = n+1, g(x) = \sqrt{x}, g(f(x)) = \sqrt{f(x)};\) agh never mind I will make it overly complicated.. I tried to show that while solving smth it really helps me to make an abstraction i.e. treat some polynomial as one unknown variable to see what operations I have to do with it...

@ramiy make sure you don't confuse this \((\sqrt{n+1})^2\) with \(\sqrt{(n+1)^2}\)

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