Question

Prove that 2+4√3 is irrational​

Answer 1

Let us assume that 4-3√2 is rational number. So we can write 4-3√2 as a/b where a and b are co primes and b is not equal to 0. 4-3√2 = a/b. ... Here √2 is an irrational number.

Answer 2

Answer :

Let 2+4√3 be rational, so, it can be expressed as p/q where, p and q are co prime numbers.

2 + 4√3 = p/q

or, 4√3 = p/q - 2

or, 4√3 = p - 2q / q

or √3 = p - 2q / 4q

Since, p , q , 2 and 4 are rational so √3 is rational.

This contradict the fact that √3 is irrational.

So, 2 + 4√3 ia irrational.