Question

Prove that this is irrational ​

Answer 1

Answer:

i

This is a problem from 2018 that was in my feed in July 2019.

Because

3>5–√,

the radicals can be unnested.

Let

3+5–√−−−−−−√=x−−√+y√.

Square both sides and get

(3+5–√−−−−−−√)(3+5–√−−−−−−√)

=(x−−√+y√)(x−−√+y√).

This means that

3+5–√=x+y+2xy−−√.

It implies that

3=x+y and 5–√=2xy−−√.

Square the latter equation and get

5=4xy.

From this

y=54x.

thanks