Question

show that 4+underoot3 is irrational​

Answer 1

Let us assume 4+√3 is rational

so, 4+√3 = p/q.

suppose, p & q have a common factor other than 1.

so, 4 + √3 =a/b,where a & b are co-prime.

4 + √3 = a/b

√3 = a/b - 4

√3 = a - 4b / b

Because, √3 is irrational

Therefore, 4 + √3 is irrational

Hence proved