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Answer variants:
\(\sqrt{19} = \frac{p}{7q}\)
\(\sqrt{19}\) is a rational
cannot be expressed as p/q form
can be expressed as p/q form
co-primes
\(7 \sqrt{19} = \frac{p}{q}\)
contradicts
composites
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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