Question

prove that 3+2√ 5 is Irrational​

Answer 1

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3 + 2√5 = a/ b

2√5 =a/b -3

√5 =a-3b/2b

√5 is rational.

This contradicta the fact that √5 is irrational.

So our supposition is incorrect.

Hope this will help you.

Answer 2

let us assume that 3+2√5 is rational.

3+2√5=a/b (where a and b are coprimes and b is not equal to 0)

3+2√5=a/b

2√5= a/b-3

2√5= a-3b/b

√5=a-3b/2b

√5 is a irrational number and a-3b/2b is rational

this is a contradiction to the fact that 3+2√5 is rational.

therefore 3+2√5 is irrational

hence proved.