Question

prove that 5+2√3 is irrational​

Answer 1

$\underline{\underline{\huge{\pink{\tt{\textbf Answer :-}}}}}$

Let us assume that 5 - 2 √3 is a rational number.

So, 5 - 2 √3 may be written as

5 - 2 √3 = p/q, where p and q are integers, having no common factor except 1 and q ≠ 0.

⇒ 5 - p/q = 2 √3

⇒ √3 = 5q - p/2q

Since, 5q - p/2q is a rational number as p and q are integers.

Therefore, √3 is also a rational number, which contradicts our assumption.

Thus, Our supposition is wrong.

Hence, 5 - 2 √3 is an irrational number.