Final answer:
An example of two irrational numbers that combine to make a rational number is √2 + √3 = 5 - 2√6.
Step-by-step explanation:
Example: Let's take the irrational numbers √2 and √3. While individually these numbers are irrational, their sum is rational. Adding √2 and √3 gives us a rational number, which is √2 + √3.
To simplify this expression, we can rationalize the denominator. Multiplying both the numerator and denominator by √2 - √3 will eliminate the irrational parts:
√2 * (√2 - √3) + √3 * (√2 - √3) = 2 - √6 + 3 - √6 = 5 - 2√6
So, the combination of √2 and √3 results in a rational number of 5 - 2√6.