Question

Prove that 7√2/3 are irrational number​

Answer 1

ANSWER:

• (7√2)/3 is an irrational number.

GIVEN:

• Irrational number = 7√2/3

TO PROVE:

• 7√2/3 is an irrational number.

SOLUTION:

Let 7√2/3 be a rational number which can be expressed in the form of p/q where p and q have no common factor other than 1.

$\implies \: \dfrac{7 \sqrt{2} }{3} = \dfrac{p}{q} \\ \\ \implies \: 7 \sqrt{2} = \frac{3p}{q} \\ \\ \implies \: \sqrt{2} = \frac{3p}{7q}$

Here; 3p/7q is rational but √2 is Irrational.

Thus our contradiction is wrong.

• So (7√2)/3 is an irrational number.

NOTE:

• This method of proving irrational number is called the contradiction method.
• In this way we can Contradict a fact and we also prove that wrong.