Question

Are these numbers rational or not?
\sqrt(72) -
pi -
\sqrt(36) -
2.7 -
\sqrt(14) -
11/23 -

Answer 1

To determine whether each number is rational or not, we need to understand that a rational number can be expressed as a fraction of two integers \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \).

1. **\(\sqrt{72}\)**:
- This can be simplified: \(\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}\).
- Since \(\sqrt{2}\) is irrational, \(\sqrt{72}\) is irrational.

2. **\(\pi\)**:
- \(\pi\) is a well-known mathematical constant that is irrational.

3. **\(\sqrt{36}\)**:
- This simplifies to \(6\), which is a whole number and thus a rational number.

4. **\(2.7\)**:
- This is a terminating decimal, which can be expressed as \(\frac{27}{10}\), making it a rational number.

5. **\(\sqrt{14}\)**:
- \(\sqrt{14}\) is irrational since 14 is not a perfect square.

6. **\(\frac{11}{23}\)**:
- This is a fraction of two integers, so it is a rational number.

In summary:
- \(\sqrt{72}\): Irrational
- \(\pi\): Irrational
- \(\sqrt{36}\): Rational
- \(2.7\): Rational
- \(\sqrt{14}\): Irrational
- \(\frac{11}{23}\): Rational