Question

Prove that 3√3 is not a rational number

Answer 1

ANSWER:

• 3√3 is an Irrational number.

GIVEN:

• Number = 3√3.

TO PROVE:

• 3√3 is an Irrational number.

SOLUTION:

Let 3√3 be a rational number which can be expressed in the form of p/q where p and q have no other common factor than 1.

$\implies \: 3 \sqrt{3} = \dfrac{p}{q} \\ \\ \implies \: \sqrt{3} = \dfrac{p}{3q}$

Here:

• p/3q is rational but √3 is an Irrational number.
• Thus our contradiction is wrong.
• 3√3 is an Irrational number.

NOTE:

• This method of proving an Irrational number is called contradiction method.
• In this method we first contradict a fact and than we prove that our supposition was wrong.
• In this way we can prove an Irrational number.