Question

prove that 6 - 4 under root 3 is an irrational number​

Answer 1

6 - 4 √3

as the value of root 3 is 1.732

which is non terminating no. hence when we calculate it it will not be appropriate or can't be calculated

hence it is an irrational no.

Answer 2

Answer:

First let us assume that 6 - 4√3 is rational.

So, 6-4√3 = a/b

where, a&b are coprime integers and b≠0

=> 6 = a/b + 4√3

=>√3 = [6-a/b]/4

= (6b - a)/4b

As a, b are integers, the r. h. s is rational.i.e,

(6b - a)/4b is rational.

So, L.H.S is also rational. i.e., √3 is rational.

But this contradicts the fact that √3 is irrational. This contradiction has arisen because we assumed that 6 - 4√3 is rational.

Therefore, 6 - 4 √3 is irrational

Hence Proved.