Question

Sums & Products of Rational Numbers Quick Check 1 of 51 of 5 Items Question According to the Closure Property, which of these sums results in a rational number?(1 point) Responses 0.643892553…+34 0.643892553 dot dot dot plus Start Fraction 3 over 4 End Fraction 0.6¯¯¯¯+910 0 point Modifying above 6 with bar plus Start Fraction 9 over 10 End Fraction 36−−√+221−−−√ Start Root 36 End Root plus Start Root 221 End Root π+4–√

Answer 1

To determine which of the given sums results in a rational number according to the Closure Property, let's analyze each option:

1. **0.643892553… + 34**:
- 0.643892553... is a rational number (as it can be expressed as a fraction).
- 34 is also a rational number.
- The sum of two rational numbers is rational, so this expression results in a rational number.

2. **0.6̅ + 9/10**:
- 0.6̅ (which is 0.666...) is a rational number (it can be expressed as 2/3).
- 9/10 is clearly a rational number.
- Thus, this sum also results in a rational number.

3. **√36 + √221**:
- √36 = 6 (which is rational).
- √221 is not a rational number (as 221 is not a perfect square).
- The sum of a rational number (6) and an irrational number (√221) is irrational, so this doesn't satisfy the closure property.

4. **π + 4–√**:
- π is irrational, and 4–√ (which is 2) is rational.
- The sum of an irrational number (π) and a rational number (2) is irrational.

In conclusion, the sum of **0.643892553… + 34** and **0.6̅ + 9/10** results in rational numbers.

So, the correct responses that produce sums resulting in rational numbers are:

- **0.643892553… + 34**
- **0.6̅ + 9/10**

Both of these options are valid according to the Closure Property.