Toggle whether the expression is rational or irrational.(9 points)

Rational Irrational
23×5–√

0.5



49−−√

0.5+34

3.5×4.3

2–√

3–√+25

2π +7

1 answer

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!