Question

Prove that 15+17 root 3 is irrational

Answer 1

Step-by-step explanation:

Let, 15+17√3 be rational.

Therefore, 15+17√3 =a/b, where a and b are integers having no common factor other than 1.

Now, 15+17√3=a/b

=>17√3 =a/b-15

=>17√3=a-15b/b

=>√3 =a-15b/17b

Since, a and b are integers, therefore √3 is rational. This contradicts the fact that √3 is irrational. Therefore, our assumption was wrong. Hence, 15+17√3 is irrational.