Question

prove that 6-root 3 is an irrational number ​

Answer 1

Answer:

Step-by-step explanation:

Since the value of root 3 is a non terminating non recurring decimal no. So 6root 3 will also be non terminating non recurring no. And hence it is an irrational no..

Answer 2

Assume that 6+2√3 is rational

6+2√3 = a/ b where a and b are co- prime integers

2√3= a-6b/b

√3= a - 6b / 2b

RHS is of the form p/ q LHS is also rational

but it Contradicts the fact that √3 is irrational due to our incorrect assumption that 6+2√3 is rational , Hence 6+2√3 is irrational.