Question

Which numbers are irrational? Check all that apply.

StartRoot 196 EndRoot
StartRoot 80 EndRoot
StartRoot 16 EndRoot
Pi
StartRoot 12 EndRoot
StartFraction 7 Over 18 EndFraction

Answer 1

To determine which numbers from the list are irrational, we first need to know what constitutes an irrational number. An irrational number is a number that cannot be expressed as a simple fraction (where both the numerator and denominator are integers). Common examples include numbers like \(\pi\) and the square roots of non-perfect squares.

Now, let's evaluate each number on your list:

1. \(\sqrt{196}\) - This is \(14\) (a perfect square, thus rational).
2. \(\sqrt{80}\) - This simplifies to \(4\sqrt{5}\), which is not an integer and since \(\sqrt{5}\) is irrational, \(4\sqrt{5}\) is irrational.
3. \(\sqrt{16}\) - This is \(4\) (a perfect square, thus rational).
4. \(\pi\) - This is known to be an irrational number.
5. \(\sqrt{12}\) - This simplifies to \(2\sqrt{3}\), and since \(\sqrt{3}\) is irrational, \(2\sqrt{3}\) is also irrational.
6. \(\frac{7}{18}\) - This is a rational number (it can be expressed as a fraction).

Now, checking the results, the irrational numbers from the list are:

- \(\sqrt{80}\)
- \(\pi\)
- \(\sqrt{12}\)

Thus, the irrational numbers are:
- \(\sqrt{80}\)
- \(\pi\)
- \(\sqrt{12}\)