Question

Prove that 3+2√5 is irrational​

Answer 1

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Answer 2

Answer:

let 3+2√5 be a rational no. in its simplest form p/q. So, according to our question:

3+2√5=p/q

2√5=p/q- 3

2√5=p - 3q/q

√5=p-3q/2q

here, the fraction is in rational form as per by our supposition but it's product is √5, which is an irrational number.

this is a contradiction which proves our supposition wrong. So, (3+2√5) is an irrational number.

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