Question

Is root 3 a polynomial?

Answer 1

Hint: In the given question, we have been asked that root 3 is a polynomial or not. In order to answer this question, we will use the definition of polynomial that says a polynomial is any algebraic expression that contains variables, exponents and constants. Polynomial simply means having many terms, thus there can be any number of terms in polynomial. Later we will rewrite root is a form of polynomial such that it will remain equal but has variable and exponent. In this way we will get the required answer.

Complete step by step solution:
We have given that,
Root 3 is a polynomial.
Root 3 can be written as \[\sqrt{3}\] .
Using the zero power identity of exponent, which states that any number to the power 0 is always equal to 1, i.e.
 \[{{\left( any\ number \right)}^{0}}=1\]
Rewritten the given term in the polynomial form, we obtained
 \[\Rightarrow \sqrt{3}=\sqrt{3}\times {{x}^{0}}\]
As we know that the variable ‘x’ has some value and any number to the power zero is always equal to 1.
Degree of the above polynomial i.e. \[\sqrt{3}{{x}^{0}}\] is zero.
Therefore,
Root 3 is a polynomial as it can also be represents as \[\sqrt{3}{{x}^{0}}\] , and the polynomial has variable ‘x’ and the exponent equals to 0 i.e. with the zero power term.

Note: In order to answer this question, students need to remember the basic concept of polynomial. We should be well aware about the definition of polynomial i.e. a polynomial is an algebraic expression that has variables constants and exponents and that can be combined by using mathematical operations such as addition, multiplication, division and subtraction.