According to the Closure Property, which of these sums results in a rational number?(1 point)

Question

Responses

π+4–√
pi plus Start Root 4 End Root

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

0.643892553…+3/4

Answer 1

To determine which of the sums results in a rational number, let's analyze each option.

1. π + √4

   • π (pi) is an irrational number. √4 = 2 is a rational number. The sum of a rational and an irrational number is irrational. Therefore, this sum results in an irrational number.

2. 0.6̅ + 9/10

   • The repeating decimal 0.6̅ represents the rational number 2/3. Adding 2/3 (the rational form of 0.6̅) to 9/10 (which is also rational) results in a rational number. Therefore, this sum results in a rational number.

3. √36 + √221

   • √36 = 6, which is a rational number. √221 is an irrational number (since 221 is not a perfect square). Adding a rational and an irrational number results in an irrational number. Therefore, this sum results in an irrational number.

4. 0.643892553… + 3/4

   • The decimal 0.643892553… appears to be a non-repeating decimal, indicating it is likely an irrational number. Adding an irrational number (if 0.643892553… is indeed irrational) to the rational number 3/4 will result in an irrational number. Therefore, this sum results in an irrational number.

From this analysis, the only sum that results in a rational number is:

0.6̅ + 9/10.