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.