is an irrational number. Check the given statement is true or false.
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 |
|
Therefore, the given statement is
Answer variants:
satisfies
co-primes
false
contradicts
cannot be expressed as p/q form
true
\(8 - \sqrt{5} = \frac{p}{q}\)
can be expressed as p/q form
\(\frac{8q - p}{q} = \sqrt{5}\)
rational Number
\(\frac{8q - p}{q}\) is rational
composites
irrational Number