Question

root3 is an irrational number prove that 2+root 3 is irrational number with steps​

Answer 1

Answer:

let us assume that 2 + root 3 is an irrational number.

2 + root 3 = a/b. where a and b are co primes and b not equal to zero

2+root3 = a/b

root3 = a/b -2

root 3 = (a-2b)/b

since a and b are integers so (a-2b)/b is rational.

Thus, root 3 is also the rational but this contradicts the fact that root 3 is irrational.So our assumption is incorrect

Hence, 2 + root 3 is irrational