Prove that 3 + 2`sqrt5` is irrational
if possible let a = 3 + 2`sqrt5` be a rational number.
Squaring a2 = (3+2`sqrt5`)2
a2 = 29 +12`sqrt5`
`sqrt5` = `(a^2 - 29)/12` ........(1)
Since a is a rational number the expression `(a^2-29)/12` is also rational number.
⇒ `sqrt5` is a rational number.
This is a contradiction. Hence, 3 + 2`sqrt5` is irrational.
Concept: Concept of Irrational Numbers
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