Question

Rational and irrational numbers online practice part 1 apply the closure property to predict the answer will the sum of squared 24 and 1/8 be an irrational irrational number

Answer 1

To determine whether the sum of the squares of 24 and \( \frac{1}{8} \) will be a rational or irrational number, we will follow these steps:

1. **Square the numbers**:
- The square of 24 is \( 24^2 = 576 \).
- The square of \( \frac{1}{8} \) is \( \left(\frac{1}{8}\right)^2 = \frac{1}{64} \).

2. **Add the squared values**:
- Now we need to add \( 576 \) and \( \frac{1}{64} \):
\[
576 + \frac{1}{64}
\]

3. **Finding a common denominator**:
- The common denominator between the whole number 576 (which can be expressed as \( \frac{576 \times 64}{64} \)) and \( \frac{1}{64} \) is \( 64 \).
- Converting \( 576 \) into a fraction:
\[
576 = \frac{576 \times 64}{64} = \frac{36864}{64}
\]

4. **Now add the fractions**:
\[
\frac{36864}{64} + \frac{1}{64} = \frac{36864 + 1}{64} = \frac{36865}{64}
\]

5. **Determine if the result is rational or irrational**:
- Since \( 36865 \) is an integer and \( 64 \) is a non-zero integer, \( \frac{36865}{64} \) is a rational number.

**Conclusion**: The sum of the squares of 24 and \( \frac{1}{8} \) is a rational number.