Question

Why is

Answer 1

Answer:

Only natural numbers (i.e., non-negative integers) can be the exponents of variables in a polynomial.

Step-by-step explanation:

The exponent of variables in a polynomial should be natural numbers ($0$, $1$, $2$, $3$, $\dots$.)

• $\sqrt{2\, x}$ is equal to $\sqrt{2}\, x^{1/2}$. In this expression, $x$ is the variable. Its exponent is $1/2$, which isn't a natural number.

• On the other hand, $\sqrt{2}\, x$ is equivalent to $\sqrt{2}\, x^{1}$. The exponent of variable $x$ is $1$, which is indeed a natural number.

$\sqrt{2\, x}$ isn't a polynomial because the exponent of variable $x$ isn't a natural number. On the other hand, $\sqrt{2}\, x$ is indeed a polynomial over the set of real numbers.