Question

prove that 3 - root 2 is irrational

Answer 1

Step-by-step explanation:

3√2is a rational number but this contradicts that √2is irrational number therefore our assumpition hense 3√2 is irrational number

Answer 2

ANSWER:

• 3-√2 is an Irrational number.

GIVEN:

• Number = 3-√2

TO PROVE:

• 3-√2 is an Irrational number.

SOLUTION:

Let 3-√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.

=> 3-√2 = p/q

=> 3-p/q = √2

=> (3q-p)/q = √2

Here:

• (3q-p)/q is rational but √2 is Irrational.
• Thus our contradiction is wrong.
• 3-√2 is an Irrational number.

NOTE:

• This method of proving an irrational number is called contradiction method.
• In this method we first contradict a fact then we prove that our superposition was wrong.
• In this way we can prove that 3-√2 is an Irrational number.