Question

10. Prove that √2 + √3 is irrational.​

Answer 1

Answer:

let assume that√2+√3 is irrational

√2+√3=a/b (here a and b are co primes)

√3=a/b-√2

(√3) ² =(a/b-√2) ² ( squaring both sides)

3=a²/b²-2a/b√2+2

2a/b√2=a²/b²-1

√2=a²-b²/2ab

since a and b are integers so a²-b²/2ab is rational

thus √2 is also rational

but this contradict the fact that√2 is irrational. so our assumption is wrong