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**Hint:**Here the given question based on the Multiplication and Division of Radicals, we have to multiply the given radicals. First we should write the radical in exponent form like \[\sqrt x = {x^{\dfrac{1}{2}}}\] after to multiply use the one of the law of indices i.e., \[{a^m} \times {a^n} = {a^{m + n}}\] and on further simplification we get the required solution.

**Complete step-by-step solution:**

The square root of a natural number is a value, which can be written in the form of \[y = \sqrt a \]. It means ‘y’ is equal to the square root of a, where ‘a’ is any natural number. We can also express it as \[{y^2} = a\].Thus, it is concluded here that square root is a value which when multiplied by itself gives the original number, i.e., \[a = y \times y\].

The symbol or sign to represent a square root is ‘\[\sqrt {} \]’. This symbol is also called a radical. Also, the number under the root is called a radicand.

Consider the data in given question

square root of x times i.e, \[\sqrt x \]----(1)

4th root of x times i.e., \[\sqrt[4]{x}\]------(2)

9th root of x times i.e., \[\sqrt[9]{x}\]------(3)

Now multiply the radicands (1), (2) and (3) together, then

\[ \Rightarrow \,\,\,\,\sqrt x \times \sqrt[4]{x} \times \sqrt[9]{x}\]

Write the radical in exponent form, then

\[ \Rightarrow \,\,\,\,{\left( x \right)^{\dfrac{1}{2}}} \times {\left( x \right)^{\dfrac{1}{4}}} \times {\left( x \right)^{\dfrac{1}{9}}}\]

By law of indices, to multiply expressions with the same base, copy the base and add the indices i.e., \[{a^m} \times {a^n} = {a^{m + n}}\], then

\[ \Rightarrow \,\,\,\,{x^{\dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{9}}}\]

Take 36 as lcm in the power

\[ \Rightarrow \,\,\,\,{x^{\dfrac{{18 + 9 + 4}}{{36}}}}\]

On simplification, we get

\[ \Rightarrow \,\,\,\,{x^{\dfrac{{31}}{{36}}}}\]

Write this in the radicand form

\[ \Rightarrow \,\,\,\,\sqrt[{36}]{{{x^{31}}}}\]

Hence, the value of \[\sqrt x \times \sqrt[4]{x} \times \sqrt[9]{x}\] is \[\sqrt[{36}]{{{x^{31}}}}\].

**Note:**The exponential number is defined as the number of times the number is multiplied by itself. It is represented as \[{a^n}\], where a is the numeral and n represents the number of times the number is multiplied. For the exponential numbers we have a law of indices and by applying it we can solve the given number.

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