prove that 3+2√5 is irrational
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suppose that 3+2root 5 is a rational number
therefore it is in the form of p/q
3+2root 5=p/q
by squaring both sides
(3+2root5)²=(p/q)²
9+20+12root5=p²/q²
29+12root5=p²/q²
12root5=p²/q²-29
root5=p²-29q²/12q²
p²-29q²/12q² is a rational but root5 is not a rational
therefore our supposition is wrong 3+2root5 is not a rational number
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