Question

Is the given expression a polynomial in one variable ? Give reasons for your answers.
$5\sqrt{x}+x\sqrt{5}$

Answer 1

The given expression is $5\sqrt{x}+x\sqrt{5}$

In a polynomial, exponent of a variable must be a whole number.

Expression with exponent of a variable in fraction and negative number is not considered as a polynomial.

Now,

$5\sqrt{x}+x\sqrt{5}$

$=5x^{\frac{1}{2}}+x\sqrt{5}$

Here, one of exponents of variable is $\frac{1}{2}$, which is a fraction.

Hence, $5\sqrt{x}+x\sqrt{5}$ is not a polynomial.