## Prove that 3 +2√5 is irrational

let us assume to the contrary that 3+ 2√5 is a rational number. So

3 + 2√5 = p/q , where p and q are coprime integers and q is not equal to zero

2√5 = p/q -3

2√5 = (p-3q)/q

√5= (p-3q)/2q

since √5 is irrational but (p-3q)/2q is rational.

And rational number can not equal to irrational number. So there is a contradiction. Our assumption is wrong, hence 3+2√5 is irrational.

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Ncert Solutions Class 10 Maths Exercise 4.3 https://10thmathsguide.com/exercise-43-class-10-maths/

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