Question

Prove that 5 - 2√3 is an irrational number.

Answer 1

Nice question

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

thank you !! sweet dreams

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Answer 2

hope it will be helpful