Question

show that 3 under root 5 is not a rational number​

Answer 1

ANSWER:

• 3√5 is an Irrational number.

GIVEN:

• Number = 3√5

TO PROVE:

• 3√5 is an irrational number.

SOLUTION:

Let 3√5 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.

$\implies \: 3 \sqrt{5} = \dfrac{p}{q} \\ \\ \implies \: 3( \sqrt{5} ) = \dfrac{p}{q} \\ \\ \implies \: \sqrt{5} = \dfrac{p}{q} \times \frac{1}{3} \\ \\ \implies \: \sqrt{5} = \dfrac{p}{3q}$

Here:

• p/3q is rational but√5 is an irrational number.
• Thus our contradiction was wrong.
• So 3√5 is an Irrational number.

NOTE:

• This method of proving and irrational number is called contradiction method
• In this method we first contradict a fact then we prove that our supposing was wrong.