Question

Prove that 3 plus 2 root 5 is the irrational?

Answer 1

to prove that 3 root 5 is irrational
if possible that 3 + 2 root 5 be rational and equal to X then
x=3+2√5
x^2=(3+2√5)^2
by identity
x^2=9+20+4√5
x^2=29+4√5
x^2-29=4√5
29-x^2/4=√5
now
X is rational
x square is rational
29-x^2/4 is rational
but √5is irrational..
3 + 2 root 5 is irrational that is. proved