Question

I was thinkin of one of the questions KingGeorge asked and accidently i got a nice problem...

Show that \(\sqrt{n+\sqrt{n+1}}\) is irrational for any given positive integer \(n\).

Answer 1

what about 1 or 0

Answer 2

for n value

Answer 3

*
for n>0 the expression is not a perfect square will suffice.

Answer 4

if n is any positive integer except perfect square numbers than (n)^(1/2) is always irrational ?

Answer 5

Yes

Answer 6

Is that right?

Answer 7

The statement is correct.

Answer 8

Then, I think the solution is no further

Answer 9

Now, for to be a rational number, also must be a rational number. Now, is a rational number if where x is positive integer. Now, . Now,...........Thus, is a irrational number.