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 |
|
Answer variants:
contradicts
can be expressed as p/q form
\(\frac{7q - p}{q}\) is rational
\(\frac{7q - p}{q} = \sqrt{31}\)
\(7 - \sqrt{31} = \frac{p}{q}\)
satisfies
rational Number
irrational Number
co-primes
composites
cannot be expressed as p/q form