Question

Prove that 3 -2√5 is an irrational number

Answer 1

Let us assume 3-2√3 is a rational.

3-2√5 = a/b

Where a, b are integers and

b≠0.

=> 2√5 = 3-a/b

=> 2√5 = (3b-a)/b

=> √5 = (3b-a)/2b

Since , a,b are integers,

(3b-a)/2b is a rational ,So ,

√5 is rational.

But this contradicts the

fact that √5 is irrational.

Therefore,

3-2√5 is an irrational.

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