Question

Toggle whether the expression is rational or irrational.(9 points)
Rational Irrational
23×5–√


0.5


7π


49−−√


0.5+34


3.5×4.3


2–√


3–√+25


2π +7

Answer 1

Let's evaluate each expression to determine whether it is rational or irrational.

1. **\( 23 \times 5 - \sqrt{} \)**
Without the complete expression (the square root part), it's difficult to classify. If we assume it means \( 23 \times 5 \) (which equals 115) minus some rational number, the answer will depend on that square root. If it’s a rational number, the whole result is rational. Without clearer details, we can't classify this.

2. **\( 0.5 \)**
This is a rational number (it can be expressed as \( \frac{1}{2} \)).

3. **\( 7\pi \)**
This is irrational, as \( \pi \) itself is an irrational number, and multiplying it by a non-zero rational number (7) keeps it irrational.

4. **\( \sqrt{49} \)**
This is rational, as \( \sqrt{49} = 7 \), which is a whole number.

5. **\( 0.5 + 34 \)**
This is rational. \( 0.5 \) is rational, and \( 34 \) is also rational, and the sum of two rational numbers is rational.

6. **\( 3.5 \times 4.3 \)**
This is rational, as both \( 3.5 \) and \( 4.3 \) are rational numbers, and the product of rational numbers is rational.

7. **\( \sqrt{2} \)**
This is irrational, as \( \sqrt{2} \) is a famous example of an irrational number.

8. **\( \sqrt{3} + 25 \)**
This is irrational. \( \sqrt{3} \) is irrational, and adding it to a rational number (25) keeps it irrational.

9. **\( 2\pi + 7 \)**
This is irrational, as \( 2\pi \) is irrational, and adding a rational number (7) keeps it irrational.

To summarize:

| Expression | Type |
|------------------------------|------------|
| \( 23 \times 5 - \sqrt{} \) | Unknown |
| \( 0.5 \) | Rational |
| \( 7\pi \) | Irrational |
| \( \sqrt{49} \) | Rational |
| \( 0.5 + 34 \) | Rational |
| \( 3.5 \times 4.3 \) | Rational |
| \( \sqrt{2} \) | Irrational |
| \( \sqrt{3} + 25 \) | Irrational |
| \( 2\pi + 7 \) | Irrational |

Feel free to let me know if you need further clarification!