Question

according to the closure property, which of these sums results in a rational number?
A. 0.643892553 . . . + 3/4
B. 0.6 + 9/10
C. √36 + √221
D. π + √4

Answer 1

To determine which of these sums results in a rational number, we need to analyze each option according to the closure property of rational numbers. Rational numbers are those that can be expressed as the quotient of two integers.

**A.** \( 0.643892553... + \frac{3}{4} \)

Here, \( 0.643892553... \) is a decimal that appears to be a non-repeating decimal. If it is a non-terminating non-repeating decimal, it would be irrational. Assuming it is rational since it has a finite number of decimal digits, we can add \( \frac{3}{4} \) (which is also rational). The sum would be rational.

**B.** \( 0.6 + \frac{9}{10} \)

Both \( 0.6 \) and \( \frac{9}{10} \) are rational numbers. Their sum will also be rational.

**C.** \( \sqrt{36} + \sqrt{221} \)

\( \sqrt{36} \) is rational (equal to 6), but \( \sqrt{221} \) is irrational. The sum of a rational number and an irrational number is irrational.

**D.** \( \pi + \sqrt{4} \)

\( \sqrt{4} = 2 \) is rational, but \( \pi \) is irrational. The sum of a rational number and an irrational number is irrational.

### Conclusion:
The sums that result in rational numbers are:

- **B.** \( 0.6 + \frac{9}{10} \)
- **A.** (if \( 0.643892553... \) is assumed to be rational, then this could also be rational).

However, based on typical properties:
- **A** may depend on the nature of \( 0.643892553...\).

So the **sure rational sum** is option **B**.