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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? Responses 0.643892553…+34 0 point 6 4 3 8 9 2 5 5 3 dot dot dot plus 3 fourths - no response given 36−−√+221−−−√ square root of 36 plus square root of 221 - no response given 0.6¯¯¯¯+910 0 line segment point 6 plus 9 tenths - no response given π+4–√ pi plus square root of 4 - no response given Skip to navigation

1 answer

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 decimal expansion that does not terminate or repeat, so it is an irrational number. However, adding a rational number (34) to an irrational number will still yield an irrational number. Result: Irrational

  2. √36 + √221

    • √36 is 6, which is rational. √221 is an irrational number. The sum of a rational number and an irrational number is irrational. Result: Irrational

  3. 0.6 + 9/10

    • Here, 0.6 (or 6/10) is a rational number (it can be expressed as 3/5) and 9/10 is also a rational number. The sum of two rational numbers is rational. Result: Rational

  4. π + √4

    • π is an irrational number and √4 is 2, which is rational. The sum of a rational number and an irrational number is irrational. Result: Irrational

Based on the analysis, the only sum that results in a rational number is:

0.6 + 9/10.