Question

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Q.1 Prove that 3+ 2/5 is irrational number​

Answer 1

Answer:

Let 3+2√5 is rational

Therefore,We can find two co-prime integers 'a' and 'b' such that

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

Therefore, a/b-3= 2√5

A-3b /b = 2√5

A-3b /2b = √5

Therefore, A and B are integers,

Therefore, a-3b /2b= Integer - 3 ( integer) / 2( integer)

a-3b/2b = Rational number

(1) is a rational

√5 is a rational

But this contradicts the fact that √5 is irrational.

Therefore, 3+2√5 is an irrational.