Question

prove that 2√3is not rational numbers​

Answer 1

Answer:

Hope this helps you.......

Answer 2

$\huge {\underline {\underline {\tt {Question:-}}}}$

$\odot$ Prove that $2\sqrt{3}$ is not rational number?

$\huge {\underline {\underline {\tt {\pink {How \: to \: solve?}}}}}$

• To know that the given digit is not a rational number then we have to assume that the given digit is rational number.
• Then using the rules and theorams of rational number we have to solve it and prove it.
• Theoram makes it easy to prove that particular digit is irrational (not a rational) .
• ☀️So, lets start.

$\huge {\underline {\underline {\tt {\blue {Answer}}}}}$

$\implies$ Let us assume , to the contrary, that $2\sqrt{3}$ is a rational number.

Now,

That ,is we can find co prime a and b ( b $\neq$ 0) such that $\tt 2\sqrt{3} = \dfrac{a}{b}$

By,.

rearranging , we get $\tt \sqrt{3} = \dfrac{a}{2b}$is rational., and so $\sqrt{3}$ is rational.

But,

this contradicts the fact that $\sqrt{3}$ is irrational.

So,

from this we can conclude that ${\red 2\sqrt{3}}$ is not a rational number

☃️Hence we are done with the problem.