Question

|(n+1)^(1/2) - n^(1/2)| = 1/((n+1)^(1/2) + n^(1/2))
Could someone explain this equality to me, having trouble. Thanks.

Answer 1

\[
\sqrt{n+1}-\sqrt{n}=\frac{1}{\sqrt{n}+\sqrt{n+1}}
\]
No need for absolute value is the quantity is positive.
Cross multuply and you get
n+1 -n = 1
You are done

Answer 2

I was trying to work out how you produce the RHS having been given the LHS

Answer 3

Them tutors always like to make life difficult!

Answer 4

\[
\sqrt{n+1}-\sqrt{n}=\frac{\left(\sqrt{n+1}-\sqrt{n}\right
)
\left(\sqrt{n+1}+\sqrt{n}\right)}{\sqrt{n+1}+\sqrt{n}}= \frac { n+1 -n}{\sqrt{n+1}+\sqrt{n}}=\\
\frac { 1}{\sqrt{n+1}+\sqrt{n}}
\]

Answer 5

Perfect. Was just googling conjugate as we spoke. Thanks very much for your time.

Answer 6

yw