Question

prove that 2√3 is a rational number

Using method:-
Contradict method​

Answer 1

$\begin{gathered}\large {\boxed{\sf{\mid{\overline {\underline {\star ANSWER ::}}}\mid}}}\end{gathered}$

To Prove :-

➪ 2√3 is an irrational number.

Solution :-

Let us assume that 2√3 is a rational number, so that it can be expressed in the form of p/q , and q≠0 .

Note :- All rational numbers can be expressed in the form of p/q, q ≠ 0.

∴ 2√3 = p/q

Dividing both sides by 2:

√3 = p/2q

➪ RHS : Clearly, p/2q is a rational number, and 2q ≠ 0.

➪ LHS : But, We already know that √3 is an irrational number, which is not possible.

Note :- Always a rational number must be equal to a rational number only.

Hence, our assumption is wrong.

This contradicts the fact that 2√3 is a rational number.

$\large\boxed{∴ \: 2 \sqrt{3} \: is \: an \: irrational \: number}$

@SweetestBitter