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Question
To which subset(s) does the number –Start Root 25 End Root belong? Choose all that apply.
(1 point)
Responses
irrational numbers
rational numbers
integers
whole numbers
The number -Start Root 25 End Root belongs to the following subsets:
irrational numbers
rational numbers
integers
whole numbers
To determine which subset(s) the number √25 belongs to, let's go through each option:
1. Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction and have non-repeating decimal representations. However, √25 is not an irrational number since it can be expressed as a whole number (5) and has a terminating decimal representation (5.00). Therefore, this subset does not apply.
2. Rational numbers: Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers, and the denominator is not zero. Since √25 can be expressed as the fraction 5/1, it is a rational number. Therefore, this subset applies.
3. Integers: Integers are whole numbers (both positive and negative) and zero. Since √25 is a positive whole number (5), it is considered an integer. Therefore, this subset applies.
4. Whole numbers: Whole numbers are non-negative integers, including zero. Since √25 is a positive whole number (5), it is considered a whole number. Therefore, this subset applies.
In conclusion, the number √25 belongs to the subsets of rational numbers, integers, and whole numbers.
To determine the subsets to which the number -√25 belongs, we can first simplify the expression. Since the square root of 25 is equal to 5, the expression becomes -5.
Now, let's analyze the options:
1. Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction or a decimal that terminates or repeats. Since -5 can be expressed as the fraction -5/1, it is not an irrational number. Therefore, this option does not apply.
2. Rational numbers: Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. Since -5 can be expressed as the fraction -5/1, it is a rational number. Therefore, this option applies.
3. Integers: Integers are whole numbers and their negative counterparts, including zero. Since -5 is a negative whole number, it is an integer. Therefore, this option applies.
4. Whole numbers: Whole numbers are non-negative integers, including zero. Since -5 is a negative number, it is not a whole number. Therefore, this option does not apply.
Based on the analysis, the number -√25 belongs to the subsets of rational numbers and integers.