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