Question

prove that 15 plus root 3 is an irrational number​

Answer 1

Answer:

we have to solve it by contradictory assumption

Step-by-step explanation:

let 15+root 3 be rational.

hence, there exists two integers co prime a and b such that

15+root 3= a/b

root 3=a/b-15

if a/b is rational then a/b-15 is also rational as a and b are integers

hence root 3 is rational.

but we know root 3 is irrational.

hence we arrive at a contradiction

this contradiction arises due to our assumption that 15+root 3 is rational

hence our assumption is wrong and

15+root 3 is irrational.