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

Rational Irrational
3–√+25

23×5–√

2π +7

0.5+34

0.5

2–√

3.5×4.3

49−−√

1 answer

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

  1. \(3\sqrt{+25\)

    • This is \(3\sqrt{25} = 3 \times 5 = 15\), which is rational.
  2. \(23 \times 5\sqrt{}\)

    • Assuming a typo and this is intended as \(23 \times \sqrt{5}\): \(\sqrt{5}\) is irrational, thus \(23 \times \sqrt{5}\) is also irrational.
  3. \(2\pi + 7\)

    • \(2\pi\) is irrational, hence \(2\pi + 7\) is irrational.
  4. \(0.5 + 34\)

    • This is \(0.5 + 34 = 34.5\), which is rational.
  5. \(0.5\)

    • This is rational (as it can be expressed as \(\frac{1}{2}\)).
  6. \(2\sqrt{}\)

    • Assuming a typo, reading it as \(2\sqrt{2}\): \(\sqrt{2}\) is irrational, hence \(2\sqrt{2}\) is also irrational.
  7. \(3.5 \times 4.3\)

    • This computes to \(15.05\), which is rational.
  8. \(49\sqrt{}\)

    • Assuming this means \(\sqrt{49}\): \(\sqrt{49} = 7\), which is rational.
  9. \(7\pi\)

    • Since \(\pi\) is irrational, \(7\pi\) is also irrational.

Summary:

  • Rational:

    • \(3\sqrt{+25} = 15\)
    • \(0.5 + 34 = 34.5\)
    • \(0.5\)
    • \(3.5 \times 4.3 = 15.05\)
    • \(\sqrt{49} = 7\)
  • Irrational:

    • \(23 \times \sqrt{5}\)
    • \(2\pi + 7\)
    • \(2\sqrt{2}\)
    • \(7\pi\)

If any of the interpretations were off, please clarify, and I can make adjustments!