Question

Prove that 3+2 root 5is irrational.
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Answer 1

√5=2.236067978

2×√5=4.472135955

3+2√5=3+4.472135955=7.472135955

Answer 2

It is an indirect proof.

Let's assume that 3+2√5 is an rational number.

Therefore 3+2√5 =p/q.

√5= p/q-3-2

√5 is irrational number

but we have assumed that 3+2√5 is a rational number

Therefore it ends with a contradiction and our assumption is wrong.

Therefore 3+2√5 is an irrational number