Prove that 5 - ? is irrational given that ? is irrational

1.	Prove that 5 - ? is irrational given that ? is irrational
Answer» Let as assume that 5-√3 is rational no. 5-√3 =a/b ( a and b is coprime no. & Integers &q≠0)5-a/b = √3 √3= 5b-a/ bSince a and b are integers ,we get 5-a/ b is rational no. But √3 is irrational no.So, our assumption was wrong .Hence 5-√3 is irrational no. Lets us assume that 5 is rational!So, subtraction of rational with irration results as irrational, so, 5-3 is irrational

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