Question

3+root2 prove that it is an irrational number.

Answer 1

Step-by-step explanation:

The proof for root 2 being irrational is widely available, so I’ll take that as a given.

If 3 + root2 is rational then it is equal to a/b where a,b are integers (3+root2 = a/b)

Rearrange to get b*root2 = a - b*3. Integers are closed under subtraction and multiplication, so set c = a-b*3 as an integer.

Rearrange again to get root2 = c/b is a rational number, but root2 is irrational.

Proof by contradiction: 3 + root2 is irrational.

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Answer 2

Answer:

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Step-by-step explanation:

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