To which subsets of the real numbers does the number √113 belong?
is it irrational numbers?
if there are anymore subsets this expression belongs to, please include it in your response.
irrational
no others
To determine the subset(s) of the real numbers to which the number √113 belongs, we need to consider different categories.
Firstly, √113 is an irrational number because it cannot be represented as a fraction (ratio) of two integers. It is a non-repeating and non-terminating decimal value.
Additionally, √113 belongs to other subsets of the real numbers, such as:
1. Real Numbers: Since √113 is a real number, it is a member of the set of all real numbers.
2. Algebraic Numbers: As an algebraic number, √113 is a solution to a polynomial equation with integer coefficients.
3. Positive Numbers: √113 is a positive number because the square root of a positive value yields a positive result.
4. Non-integer Numbers: √113 is a non-integer, as it is not a whole number or a fraction.
To summarize, the number √113 belongs to the subsets of the real numbers, irrational numbers, real numbers, algebraic numbers, positive numbers, and non-integer numbers.
To determine which subsets of the real numbers the number √113 belongs to, we first need to understand what the real numbers are and the subsets within them.
The real numbers consist of rational numbers and irrational numbers. Rational numbers can be expressed as fractions or ratios of two integers, while irrational numbers cannot be expressed in this form and have non-repeating, non-terminating decimal representations.
Now, let's determine if √113 is a rational or irrational number. To do this, we need to check if the square root of 113 can be expressed as a fraction.
In this case, after evaluating √113, we find that it is an irrational number. This means it cannot be expressed as a simple fraction and has a decimal representation that does not terminate or repeat.
So, yes, √113 belongs to the subset of irrational numbers within the real numbers.
Additionally, since √113 is a real number, it also belongs to the set of real numbers as a whole.
To summarize, the number √113 belongs to the following subsets of the real numbers:
1. Irrational numbers
2. Real numbers