Question

prove that 3+2√5 is a irrational number
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Answer 1

Answer:

I hope this will help you

Answer 2

Answer:

let us assume on the contrary that 3+2√5 is rational then there exist co-prime positive integers a and b such that

3+2√5=a÷b

2√5=a÷b-3

√5=a-3b÷2b

√5 is rational (a, b are integers thus, a-2b÷2b is a rational)

this contradict the fact that √5 is irrational. so let supposition is incorrect. hence, 3+2√5 is an irrational number