Question

3/2√2 is irrational​

Answer 1

Yes

As √2 is irrational no. and when an irrational no. performs any mathematical operation it results in irrational no.

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Answer 2

ANSWER:

• 3/2√2 is an irrational number.

GIVEN:

• Number = 3/2√2

TO PROVE:

• 3/2√2 is an irrational number.

SOLUTION:

Let 3/2√2 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.

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

• Here 3q/2p is rational but √2 is Irrational.
• Thus our contradiction is wrong.
• So 3/2√2 is an irrational number.

NOTE:

• This method of proving an irrational number is called contradiction method.
• In this method we contradict a fact and and we prove that it is wrong .