Question

prove that 2 - under root 3 is irrational number.​

Answer 1

$\green{\underline\textbf{To prove...}}$

✰✰ 2 - √3 as a irrational number...

$\green{\underline\textbf{SoLution...}}$

Let us assume that :-

2 - √3 is a rational number.

Let , 2 - √3   = r , where "r" is a rational number

Squaring both sides ,

[2 - √3 ]² = r²

2² - 2 x 2 x √3 + [√3]²  = r²

4 - 4√3 + 3 = r²

7 - 4√3 = r²

4√3 = r² - 7

√3 = r² - 7 ÷ (-4)

So , 

we see that LHS is purely irrational.

But , on the other side , RHS is rational.

This contradicts the fact that 2 - √3 is rational.

Hence , our assumption was wrong...

Therefore, 2 - √3 is a irrational number...