Question

Read each statement carefully. Then select if the result of the statement will be rational or irrational. (3 points) Rational Irrational The sum of two rational numbers is always the result what type of number? The sum of a rational and irrational number will result in what type of number? The product of a nonzero rational number and an irrational number will result in what type of number?

Answer 1

Let's evaluate each statement regarding the type of numbers:

1. **The sum of two rational numbers is always the result what type of number?**
- **Result:** Rational
- **Explanation:** The sum of two rational numbers is always rational because the sum of two fractions (which represent rational numbers) can be expressed as another fraction.

2. **The sum of a rational and irrational number will result in what type of number?**
- **Result:** Irrational
- **Explanation:** The sum of a rational number and an irrational number is always irrational. This is because adding a rational number to a value that cannot be expressed as a fraction (irrational) does not result in a fraction.

3. **The product of a nonzero rational number and an irrational number will result in what type of number?**
- **Result:** Irrational
- **Explanation:** The product of a nonzero rational number and an irrational number is always irrational. If you multiply a rational number by an irrational number, the result cannot be expressed as a fraction.

In summary:

1. Rational
2. Irrational
3. Irrational