Question

prove tha 3 is iirrational ​

Answer 1

Answer:

yes 3is irrational because it is not even

Step-by-step explanation:

easy meathod

Answer 2

${\bf{\red{\underline{Correct Question:}}}}$

${\bf{\blue{\underline{\bigstar\:Prove \: that \: \sqrt{3} \: is \: irrational:}}}}$

${\bf{\green{\underline{Now:}}}}$

• Let us suppose that √3 is rational number which means it can be written in the form √3=a/b where a and b are comprime.

So,

$\implies{\tt{b \sqrt{3} = a}} \\ \\ </p><p></p><p>$

$\implies{\tt{ {b}^{2} \times 3= {a}^{2} \: (\diamond \: squaring \: both \: side)}}$

$\implies{\tt{3 {b}^{2} = {a}^{2} }}$

$\implies{\tt{ {b}^{2} = \frac{ {a}^{2} }{3} }}$

${\bf{\blue{\underline{which \: means \: 3\: divides \: {a }^{2} \: and \: also \: \: 3 \: divides \: b:}}}}</p><p>$

• Because if a prime number p divides a² then it divides a also where a is positive integer.

◍Then it means 3 is a factor of a which is contradiction to our statement that a and b are coprime and have only 1 as factor.

${\bf{\blue{\underline{Therefore \: \sqrt{3} \: is \: irrational.}}}}</p><p>$