To which subset(s) does the number –square root of twenty belong? Choose all that apply.
(Irrational Numbers
(Rational Numbers***
(Integers***
(Whole Numbers
(Natural Numbers
The maximum of choices is 2
2 sqrt 5 = sqrt 20
sqrt 5 = 2.236067977
IRRATIONAL
http://www.dictionary.com/browse/irrational--number
To determine the subset(s) to which the number -√20 belongs, we need to understand the terms and definitions of each subset.
1. Irrational Numbers: These are numbers that cannot be expressed as a fraction of two integers and have an infinite number of non-repeating decimals. Examples include √2, √3, and π.
2. Rational Numbers: These are numbers that can be expressed as a fraction of two integers. Rational numbers can be terminating (e.g., 0.5) or repeating decimals (e.g., 1.3333...). Examples are 1, 0, -5/7, and 3.25.
3. Integers: These include all whole numbers and their negatives, including zero. Examples are -2, -1, 0, 1, 2, etc.
4. Whole Numbers: These include all positive integers (natural numbers) and zero. Examples are 0, 1, 2, 3, etc.
5. Natural Numbers: These are the counting numbers, starting from 1 and excluding zero. Examples are 1, 2, 3, 4, etc.
Now, we can analyze the given number, -√20:
-√20 is an irrational number because it cannot be expressed as a fraction of two integers and has a non-repeating decimal.
-√20 is also a real number because it exists on the number line.
As for the subsets, we can conclude that the number -√20 belongs to the following:
1. Irrational Numbers: Because -√20 is an irrational number.
2. Integers: Because -√20 is an integer.
Therefore, the correct answer would be both (Irrational Numbers) and (Integers).
THINK
square root of 2 (about 1.414213562) can NOT be expressed as a ratio of two whole numbers
square root of ten can NOT be expressed as ratio of two whole numbers
THEREFORE
square root of two * square root of ten which is square root of twenty can NOT be expressed as the ratio of two whole numbers
THEREFORE
square root of twenty is IRRATIONAL