Respuesta :
Answer:
1/2 +0.5=1 and 3√16 + 3√16=6√16
Step-by-step explanation:
Rational numbers are numbers that can be written as fractions. These include fractions, decimals, integers and whole numbers, or anything that can be simplified to one of these.
1/2 + 0.5 = 1 shows us a fraction added to a decimal that equals a whole number. All three of these are rational numbers, so this shows that rational numbers are closed under addition.
3√16 + 3√16=6√16 contains a radical, which is only a rational number if it simplifies to one. √16 = 4; this means we can rewrite this as
3(4) + 3(4) = 6(4)
This gives us
12 + 12 = 24
This is a true statement, and shows that rational numbers are closed under addition.
The correct equations that support the fact that rational numbers are closed under addition are;
Option C; 1/2 + 0.5 = 1
Option D; 3√16 + 3√16 = 6√16
The sum of two rational numbers is closed under the operation of addition if the sum of any two rational numbers is always equal to another rational number and is therefore in the set of rational numbers.
Let us look at the options;
Option A; 3√5 + √5 = 4√5
A rational number is a number that can be written as the fraction of two non-zero integers.
√5 cannot be written as a product of two non-zero integers. Thus, this option is not correct.
Option B; √10 + (-√10) = 0
√10 cannot be written as a product of two non-zero integers. Thus, this option is not correct.
Option C; 1/2 +0.5 = 1
All three numbers are rational numbers and thus the option is correct
Option D; 3√16 + 3√16 = 6√16
√16 is equal to 4 which is a rational number and thus this option is correct.
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