Question

Prove that 3√5 is a irrational no?

Answer 1

Answer:

Given:

• number 3√5

To prove:

• the given number is irrational.

Solving question:

Rational number : The number which can be written in the form of p/q , where q ≠ 0 and 'p' and 'q' are integers.

Irrational numbers : The numbers which cannot be  written in the form of p/q , where q ≠ 0 and 'p' and 'q' are integers.

Contradiction method : It is a type of method in which first we assume something then we prove that our assumption is wrong.

        We are going to prove it using contradiction method

Solution (Proof):

Let 3√5 be a rational number

∴ 3√5 = p/q [ where q ≠ 0 and 'p' and 'q' are integers.]

divide the whole by 3

⇒ √5 = p/3q

     Since 'p' and 'q' are integers p/3q should be a rational  , but this contradicts the fact that √5 is a irrational number.This contradiction have come due to our incorrect assumption that 3√5 is a rational number.Hence it is a irrational number.