To determine the degree of the polynomial [tex]\(\sqrt{5}\)[/tex], let's consider the definition of a polynomial and the degree of a polynomial.
A polynomial is an expression consisting of variables and coefficients, constructed using only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. The degree of a polynomial is the highest power of the variable in the polynomial.
Now, let's analyze the given polynomial [tex]\(\sqrt{5}\)[/tex]:
1. Identify the terms and variables:
The expression [tex]\(\sqrt{5}\)[/tex] is a constant because it does not contain any variables. It is just a number, even though it is a square root.
2. Determine the degree:
Since [tex]\(\sqrt{5}\)[/tex] does not contain any variable terms, it can be considered to be multiplied by [tex]\(x^0\)[/tex] (where [tex]\(x\)[/tex] is the variable and raising it to the power of 0 means any non-zero number to the power of zero is 1).
Hence, the expression [tex]\(\sqrt{5}\)[/tex] can be represented as:
[tex]\[
\sqrt{5} = \sqrt{5} \cdot x^0
\][/tex]
In this representation, the highest power of the variable [tex]\(x\)[/tex] is 0.
Therefore, the degree of the polynomial [tex]\(\sqrt{5}\)[/tex] is [tex]\(0\)[/tex].
