To determine if the sums result in a rational number, we need to understand the closure property of rational numbers. The closure property states that the sum or product of any two rational numbers is also rational.
Now let's break down the sums you listed:
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5 + √4:
- √4 = 2, so 5 + √4 = 5 + 2 = 7, which is rational.
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0.643892553...:
- This number is a decimal and appears to be irrational because it does not terminate or repeat. Thus, adding it to a rational number would not guarantee a rational result.
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3/4:
- This is a rational number.
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0.6 + 9/10:
- Convert 0.6 to a fraction: 0.6 = 6/10 = 3/5.
- 9/10 is also a rational number.
- 3/5 + 9/10 can be converted to a common denominator:
- 3/5 = 6/10, so 6/10 + 9/10 = 15/10 = 3/2, which is rational.
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36 + √221:
- √221 is not a perfect square and is an irrational number.
- Thus, 36 (a rational number) + √221 (an irrational number) results in an irrational number.
Based on the above analysis, the sums that result in a rational number are:
- 5 + √4 = 7
- 0.6 + 9/10 = 3/2
The other two do not yield rational numbers.
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