Question

prove that √2+√3 is irrational.​

Answer 1

Answer:

Let √2 + √3 = (a/b) is a rational no. On squaring both sides , we get 2 + 3 + 2√6 = (a2/b2) So,5 + 2√6 = (a2/b2) a rational no. So, 2√6 = (a2/b2) – 5 Since, 2√6 is an irrational no. and (a2/b2) – 5 is a rational no. So, my contradiction is wrong. So, (√2 + √3) is an irrational no.

Answer 2

Let us assume that √2+√3 is rational. it can be expressed in the form a/b where a and b are integers and b is not equal to zero.

√2+√3=a/b

√3=a/b-√2

√3=a-√2b/b

since, a and b are integers , therefore, a-√2b/b is rational which means that √3 is rational. but this contradicts the fact that √3 is irrational. this contradiction has arisen due to our incorrect assumption that √2+√3 is rational

so we conclude that √2+√3 is irrational.