Question

prove that 2+5√3 is an irrational number?​

Answer 1

Step-by-step explanation:

Let, us assume that 2+5√3 is a rational number.

Therefore, 2+5√3=a/b (where a and b are co prime)

5√3=a/b-2

5√3=a-2b/b

√3=a-2b/5b

Therefore, a-2b/5b is in the form of a/b which is rational number.

But,this is contradicts the fact is that √3 is irrational number.

Therefore, our assumption is wrong and 2+5√3 is an irrational number.

Hope this will help you...!!!