Question

Prove that (5 - √3) is irrational. *

Answer 1

Answer:

let us assum that 5-√3 is rational number so we can find two integers a , b. Where a and b are two co - primes number.

= 5-√3 = a/b

= √3= 5- a/b

=> a and b are integers so (5 - a/b ) is rational

But √3 is irrational ( we know that and it is given)

So it arise contradiction due to our wrong assumption that 5 - √3 is rational number.

Hence, 5 -√3 is irrational number.