irrational or rational

Question

11/12*9/22
√5*8
3+√12
π+(-2π)
-3/8+3/5
√6/2+(-1/2)

Answer 1

Let's analyze each of the given expressions to determine if they are rational or irrational.

1. \( \frac{11}{12} \times \frac{9}{22} \):

   • This is the product of two rational numbers. The result of multiplying two rational numbers is also rational.
   • Answer: Rational

2. \( \sqrt{5} \times 8 \):

   • \( \sqrt{5} \) is irrational, and multiplying an irrational number by a rational number (8 in this case) results in an irrational number.
   • Answer: Irrational

3. \( 3 + \sqrt{12} \):

   • \( \sqrt{12} \) can be simplified to \( 2\sqrt{3} \), which is irrational. Adding a rational number (3) to an irrational number results in an irrational number.
   • Answer: Irrational

4. \( \pi + (-2\pi) \):

   • This simplifies to \( \pi - 2\pi = -\pi \), which is still irrational (since π is irrational).
   • Answer: Irrational

5. \( -\frac{3}{8} + \frac{3}{5} \):

   • This is the sum of two rational numbers. The result will also be rational.
   • Answer: Rational

6. \( \frac{\sqrt{6}}{2} + \left(-\frac{1}{2}\right) \):

   • \( \frac{\sqrt{6}}{2} \) is irrational (since \( \sqrt{6} \) is irrational), and adding a rational number (-1/2) to it results in an irrational number.
   • Answer: Irrational

To summarize:

1. Rational
2. Irrational
3. Irrational
4. Irrational
5. Rational
6. Irrational