Question

Prove that 2 under root 3 upon 5 is irrational

Answer 1

We have to prove that 2√3 / 5 is an irrational number.

Here we must prove it by a contradiction.

To get a contradiction, first we assume that 2√3 / 5 is a rational number.

Now we represent 2√3 / 5 as a rational number by a letter. So let x = 2√3 / 5, where x is rational.

So, consider this equality.

x = 2√3 / 5

Multiply both sides by 5.

5x = 2√3

Now divide both sides by 2.

5x / 2 = √3

Consider this equality. At LHS, since x is rational, then so will be the LHS 5x / 2. But the RHS √3 is irrational.

Here we actually see that √3 is written in p/q form.

Hence proved that 2√3 / 5 is irrational.