Question

prove that 3 + root 2 is an irrational number​

Answer 1

let 3+√2 be a rational number

3+√2= p/q

√2 = p/q-3

And we know that the difference of rational number is rational but here the difference is irrational.

So Our Assumption is wrong.

3+√2 is an irrational number

Answer 2

let x = 3+√2

let x be a rational no.

x2 =9+2+2×3×√2

x2= 11+6√2

if x is rational then x2 is also rational

11 is rational 6 is rational

2 is irrational

so we came across a contradiction x is an irrational no.

hope you will find it helpful
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