Question

Why is


`√(2x)`
is not a polynomial but

`√(2)x`
is a polynomial?​

Answer 1

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

Explanation:

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

• 
  `√(2\, x)` is equal to
  `√(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,
  `√(2)\, x` is equivalent to
  `√(2)\, x^(1)`. The exponent of variable
  `x` is
  `1`, which is indeed a natural number.

`√(2\, x)` isn't a polynomial because the exponent of variable
`x` isn't a natural number. On the other hand,
`√(2)\, x` is indeed a polynomial over the set of real numbers.