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Prove that \(\frac{2}{13}\sqrt{3}\) is an irrational number.
Answer variants:
cannot be expressed as p/q form
\(\frac{2}{13}\sqrt{3} = \frac{p}{q}\)
contradicts
\(\frac{13}{2}\left(\frac{p}{q}\right)\) is rational
composites
co-primes
\(\frac{13}{2}\left(\frac{p}{q}\right) = \sqrt{3}\)
can be expressed as p/q form, q ≠ 0
satisfies
irrational Number
rational Number
Let's prove is an irrational number.
Now prove by contradiction method.
| 1. | Assume is a | |
| 2. | By the definition, | |
| 3. | And \(p\) and \(q\) are | |
| 4. | So we can write it as | |
| 5. | Simplifying the term, | |
| 6. | This implies that, | |
| 7. | This | our assumption. |
| 8. | Thus, is |
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