Question

Prove that
$5 - \sqrt[2]{3}$
Is irrational number
​

Answer 1

hi mate your question is,

to prove: 5-2√3 is an irrational number.

solution:- let us assume that 5-2√3 is a rational number.

so, 5-2√3 = p/q

-2√3 = p/q - 5

-2√3 = p-5q/ q

√3 = p-5q/2q

but this contradicts the fact that 5-√3 is a rational number. p-5q/2q is a rational number but √3 is an irrational number so they irrational number is not equal to rational number.

therefore, our assumption is wrong

5-2√3 is an irrational number

hence proved