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

Question

Rational Irrational
3–√+25

23×5–√

2π +7

0.5+34

0.5

2–√

3.5×4.3

49−−√

7π

Answer 1

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!