Question

is 2 minus under root 5 is rational number.

Answer 1

Hello Friend!

No, 2 - root 5 is irrational

Proving :

$let \: x = 2 - \sqrt{5} \\ {x}^{2} = {(2 - \sqrt{5}) }^{2} \\ {x}^{2} = 4 + 5 - 4 \sqrt{5} \\ {x}^{2} - 9 = - 4 \sqrt{5} \\ 9 - {x}^{2} = 4 \sqrt{5} \\ \frac{9 - {x}^{2} }{4} = \sqrt{5}$

Here, ( 9 - x^2 ) / 4 is rational which is equivalent to root 5
But we arrise at contradiction that root 5 is irrational number.

Hence proved☺!