Question

Which numbers are​ irrational?
StartRoot 64 EndRoot
StartRoot 23 EndRoot
StartRoot 100 EndRoot
StartRoot 42 EndRoot
Question content area bottom
Part 1
Which numbers are​ irrational? Select all that apply.
A.StartRoot 42 EndRoot
StartRoot 42 EndRoot
B.StartRoot 100 EndRoot
StartRoot 100 EndRoot
C.StartRoot 64 EndRoot
StartRoot 64 EndRoot
D.StartRoot 23 EndRoot
StartRoot 23 EndRoot

Answer 1

To determine which numbers are irrational, we need to consider whether the square roots of the given numbers are perfect squares or not:

1. \(\sqrt{64} = 8\) (rational, because 8 is an integer)
2. \(\sqrt{100} = 10\) (rational, because 10 is an integer)
3. \(\sqrt{42}\) (not a perfect square, so it is irrational)
4. \(\sqrt{23}\) (not a perfect square, so it is irrational)

Now we can summarize the results:

- A. \(\sqrt{42}\) - **Irrational**
- B. \(\sqrt{100}\) - **Rational**
- C. \(\sqrt{64}\) - **Rational**
- D. \(\sqrt{23}\) - **Irrational**

**Irrational Numbers:**
- A. \(\sqrt{42}\)
- D. \(\sqrt{23}\)

The numbers that are irrational are A and D.