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Which equations support the fact that rational numbers are closed under subtraction? Select each correct answer
a, √8 - √8 = 0
b, 5√4 - √4 = 4√4
c, 5.5 - 0.5 = 4
d, 2√3 - √3 = √3

Respuesta :

DeanR

The rationals being closed under subtraction means that if we start with two rational numbers and subtract them, we get another rational number.  Choice c subtracts two rational numbers but gets the wrong answer, so isn't support for anything.  Choice b is rational too because the square root of 4 is 2.

Answer: b

fichoh

A rational number is said to be closed if the subtracted values and the result obtained are rational. Hence, the equations which supports the condition are :

  • 5.5 - 0.5 = 4
  • 5√4 - √4 = 4√4

Evaluating the options :

A.)

√8 - √8 = 0 ; the added values aren't rational and the result, Zero is not rational either.

B.)

5√4 - √4 = 4√4

5(2) - 2 = 2(2)

10 - 2 = 4

All the values in the expression are rational ; hence, it supports the assertion.

C)

5.5 - 0.5 = 4 ; all the values in the expression are rational, hence, it supports the fact.

2√3 - √3 = √3 ; the values in the expression are not rational, hence, it does not meet the condition.

Therefore, only options B and C supports the assertion.

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