Step-by-step explanation:
Let √2 + √3 be a / b.
a and b are co - primes.
a and b have 1 as a common factor.
√2 + √3 = a / b
( √2 + √3 )^2 = ( a / b )^2
(√2)^2 + (√3)^2 + 2.√2.√3 = a^2 / b^2
2 + 3 + 2.√2.√3 = a^2 / b^2
5 + 2.√2.√3 = a^2 / b^2
2.√2.√3 = ( a^2 / b^2 ) - 5
2.√2.√3 = ( a^2 - 5b^2 ) / b^2
√2.√3 = ( a^2 - 5b^2 ) / 2b^2
a and b are not co - primes, as they more than 1 as a common factor.
So,
√2 + √3 is irrational.
Hence, proved.
