Your mission: justify and connect
Start with arguments and operations. Then explore logarithms, right triangles, and finance as complementary connections. Finance topics don’t always involve irrational results: an entire power with a rational basis remains rational. The number e appears in continuous growth models.
Operations challenge
Are the sum and product of two irrational numbers always irrational? Test √2 + (−√2) and √2 × √2.
Check out the investigation
No. The sum is 0 and the product is 2, both rational. A contrary example is enough to refute the statement that this always happens.
To conclude: differentiate example, conjecture and demonstration when explaining a property of numbers.