Question

how to show 4/root 3 as irrational

Answer 1

first prove that root 3 is an irrational number then you can write that the division of a rational number and an irrational number is always irrational number. therefore 4 / under root 3 is an irrational number

Answer 2

Let us assume 4/root3 as rational
So we get
4/root3=a/b
Where a and b are Co primes and b is not equal to zero
By cross multiplication we get
Root3*a=4b
Root3=4b/a
We know that 4b/a is rational
Therefore root3 is also irrational
But this contradict the fact that root3 is irrational
This Contradiction arised due to our wrong assumption that 4/root3 is rational
So we conclude that 4/root3 is irrational

Sorry for any mistake, if there is.