Classify the square root of 17 by the subsets of the real numbers to which it belongs select all that apply. Whole rational real natural integer irrational
sqrt (17)
real
not natural
not whole
not rational
not integer
irrational
Well, the square root of 17 definitely falls into the irrational subset of the real numbers. Why? Because it cannot be expressed as a fraction or a whole number. It's like an unpredictable clown jumping out of nowhere, adding a touch of chaos to the mathematical universe! So, the answer is irrational.
To classify the square root of 17, we need to determine which subsets of the real numbers it belongs to.
1. Whole numbers: The square root of 17 is not a whole number because it is not a perfect square, so it does not belong to this subset.
2. Rational numbers: A rational number can be expressed as a fraction, and the square root of 17 is an irrational number because it cannot be expressed as a fraction. Therefore, it does not belong to this subset.
3. Real numbers: The square root of 17 is a real number because it exists on the real number line. So it belongs to this subset.
4. Natural numbers: Natural numbers are positive whole numbers, and the square root of 17 is not a whole number. Therefore, it does not belong to this subset.
5. Integer numbers: Integers are whole numbers, including both positive and negative numbers, but the square root of 17 is not a whole number. Hence, it does not belong to this subset.
6. Irrational numbers: The square root of 17 is an example of an irrational number because it cannot be expressed as a fraction. Therefore, it belongs to this subset.
In summary, the square root of 17 belongs to the subsets of real numbers and irrational numbers.
To classify the square root of 17 by the subsets of the real numbers, we need to determine which of the given subsets it belongs to:
1. Natural Numbers: Natural numbers are the counting numbers (1, 2, 3, ...). The square root of 17 is not a natural number since it is not a perfect square.
2. Whole Numbers: Whole numbers include natural numbers and zero. The square root of 17 is not a whole number.
3. Integers: Integers include both positive and negative whole numbers, as well as zero. The square root of 17 is not an integer.
4. Rational Numbers: Rational numbers are numbers that can be expressed as a fraction (where the numerator and denominator are integers). The square root of 17 is not a rational number because it cannot be expressed as a fraction.
5. Irrational Numbers: Irrational numbers are numbers that cannot be expressed as a fraction and have non-terminating and non-repeating decimal representations. The square root of 17 falls into this category because it is a non-repeating and non-terminating decimal.
Therefore, the square root of 17 belongs to the subset of real numbers known as irrational numbers.