Question

prove that √3+√4 is an irrational number​

Answer 1

let's assume that √3+√4 is rational

√3+√4=a

squaring both sides

[√3+√4]^2 =a^2

3+2√12+4=a^2

7+2√12=a^2

2√12=a^2 - 7

√12=(a^2 - 7)/2

we know that √12 is irrational ,that is LHS is irrational

hence RHS is also irrational.

therefore√3+√4 is irrational.

hope this helps..