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If (\sqrt{3}) were rational, what impossible situation would appear at the end of the proof?

Answer and explanation

Correct answer: The numerator and denominator of a lowest-form fraction would both be divisible by (3)

Step 1: In the rational assumption, (\sqrt{3}=\frac{p}{q}) is taken in lowest form. Step 2: The proof gives both (3\mid p) and (3\mid q). Step 3: This is impossible in lowest form, so the assumption is false.

Related tags

Real-NumbersRoot3Impossible-ResultContradictionProof Of Irrationality Of √2√3√5Proof Of Irrationality Of 2 3 5Real NumbersMathematics

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