|(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.

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.

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Them tutors always like to make life difficult!

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

yw