Let 7 – √5 is a rational number.
7 + √5 = a/b, b ≠ 0 …(i)
Where a and b co-prime integer number.
Equation (i) can be written as
√5 = a/b – 7
or √5 = (a - 7b)/b ….(ii)
Since, a and b are integers.
So (a - 7b)/b will be rational number, so from equation (ii) we find that √5 is a rational number.
But we know that √5 is a irrational number.
So this result is contradicted.
So our hypothesis is wrong.
Hence 7 + √5 is a rational number.
