Question

Which of the following are rational numbers?

The square root of 144

The square root of 16

846.8 repeated

789.892

Answer 1

To determine whether the numbers listed are rational or not, we need to recall that rational numbers are those that can be expressed as the quotient of two integers (i.e., in the form \( \frac{a}{b} \), where \( a \) and \( b \) are integers, and \( b \neq 0 \)).

Let's evaluate each option:

1. **The square root of 144**:
\[
\sqrt{144} = 12
\]
\( 12 \) is an integer and thus a rational number.

2. **The square root of 16**:
\[
\sqrt{16} = 4
\]
\( 4 \) is also an integer and thus a rational number.

3. **846.8 repeated**:
The decimal \( 846.8 \) repeated (often written as \( 846.8888...\)) can be expressed as \( 846 + \frac{8}{90} = 846 + \frac{4}{45} \), which can be represented as a fraction, so it is a rational number.

4. **789.892**:
This is a finite decimal and can also be expressed as the fraction \( \frac{789892}{1000} \). Therefore, it is a rational number as well.

In summary, all of the following are rational numbers:

- The square root of 144
- The square root of 16
- 846.8 repeated
- 789.892