Question

According to the closure Property, which of these sums results in a rational number

sqr 36 + sqr 221
0.643892553... + 3/4
0.6repeating + 9/10
pi + spr 4

Answer 1

To determine which of the given sums results in a rational number, we'll analyze each option individually.

1. **sqr 36 + sqr 221**:
- \( \sqrt{36} = 6 \) (which is rational)
- \( \sqrt{221} \) is not a perfect square, and thus it is irrational.
- The sum of a rational number (6) and an irrational number (\(\sqrt{221}\)) is irrational.
- **Result**: Irrational.

2. **0.643892553... + 3/4**:
- \( 3/4 \) is a rational number.
- \( 0.643892553... \) appears to be a decimal representation of a real number. Since the decimal does not terminate or repeat, it is likely an irrational number.
- The sum of a rational (3/4) and an irrational number (0.643892553...) is irrational.
- **Result**: Irrational.

3. **0.6 repeating + 9/10**:
- \( 0.6 \text{ (repeating)} = \frac{2}{3} \) (which is rational).
- \( 9/10 \) is also a rational number.
- The sum of two rational numbers (\(\frac{2}{3} + \frac{9}{10}\)) is rational.
- **Result**: Rational.

4. **pi + spr 4**:
- \( \pi \) is an irrational number.
- \( \sqrt{4} = 2 \) (which is rational).
- The sum of a rational number (2) and an irrational number (\(\pi\)) is irrational.
- **Result**: Irrational.

In conclusion, the only sum that results in a rational number is:

**0.6 repeating + 9/10**.