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# Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer:$ 3 \sqrt{x}+\sqrt{2} x $

Given:

The given expression is \( 3 \sqrt{x}+\sqrt{2} x \).

To do:

We have to find whether the given expression is a polynomial in one variable.

Solution:

Polynomials:

Polynomials are expressions in which each term is a constant multiplied by a variable raised to a whole number power.

\( 3\sqrt{x}+\sqrt2 x \) can be written as $3x^{\frac{1}{2}}+\sqrt2 x$. Here, the variable in the term $3x^{\frac{1}{2}}$ is raised to the power $\frac{1}{2}$ which is not a whole number.

Therefore, \( 3\sqrt{x}+\sqrt2 x \) is not a polynomial.

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