Question

Prove that root 3 is irrational number​

Answer 1

$\huge\tt\orange{♬•Answer:}$

Let $\sqrt{3}$ be a rational no. Whose simplest form is $\huge \frac{a} {b}$.

Then, a and b are integers having no common factor other than 1 and b≠0

Now, $\sqrt{3}$ = $\huge \frac{a} {b}$

=3= $\huge \frac{a²} {b²}$

=3b²=a²________(i)

Here,3 divides a² means it will also divide a

Let a=3c for some value c

Now,putting the value a=3c in (i),we get

3b²=9c²

b²=3c²

Here 3 divides b

Now,we can see that 3 divides both a and b

But,see at the top,we declared a and b having no common factor other than 1

but ,it is contradictory , so $\sqrt{3}$ is not a rational no., it must be an irrational number..

Hence, proved that $\sqrt{3}$ is irrational

Answer 2

This is another answer , but the same thing ... plz thank me if helped ...