Question

17. Prove that 5-2√3 is irrational,​

Answer 1

Answer:

let,

5 - 2√3 be a rational number.

.°. 5 - 2√3 = p/q [ where p and q are integer , q ≠ 0 and q and p are co- prime number ]

=> - 2√3 = p/q -5

=>- 2√3 = p - 5q / q

=> √3 = p - 5q / - 2q

we know that p/q is a rational number.

.°. √3 is also a rational number.

This contradicts our assumption

5 - 2√3 is an irrational number