Question

prove that 1/2+√3 is irrational number​

Answer 1

HOPE YOU UNDERSTAND !!!!

LET ASSUME THAT I/2 + √3 IS RATIONAL NUMBER.

1/2+√3 = a/b ( a and b are co - prime number ).

we know that 1/2 is in the form of rational number.

AND√3 IS AN IRRATIONAL NUMBER.

SO OUR ASSUMPTION IS WRONG.

HENCE, 1/2+√3 IS AN IRRATIONAL NUMBER..

Answer 2

Answer:

$\huge \mathbb{\purple{Question}}$

prove that 1/2+√3 is irrational number

$\huge \mathbb{\purple{Answer}}$

Assume that 1/2+√3 is rational

$let \: \: \frac{1}{2} + \sqrt{3} \: \: be \: rational \: \: number \:$

A rational number can be written in the form of p/q where p and a are integers.

$\frac{1}{2} + \sqrt{3} = \frac{p}{q} \\ \\ \sqrt{3} = \frac{p}{q} - \frac{1}{2} \\ \\ \sqrt{3} = \frac{(2p - q)}{2q}$

P, q are integers so,

$\frac{(2p - q)}{2q}$

Is rational number.

Then

$\sqrt{3}$

Is also rational number.

But the contradicts the fact that

$\sqrt{3}$

Is an irrational number

So,

Our assumption was incorrect.

Therefore,

1/2+√3 is irrational number