Question

Prove that √2 + √3 is irrational​

Answer 1

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.