Question

How do you simplify $${\left( 3 \right)^{\dfrac{1}{4}}}$$?

Answer 1

Hint: Here in this question, we have given a number. The terms which involve this term are in the exponential form. The exponential form is written in the form of the numeral and then we have to apply the property of exponent and arithmetic operations. Hence on further simplification we obtain the required solution for the question.

Complete step by step solution:
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.
Now consider the question, the question is the form of exponential and we have to simplify it and we have to write in simplest form and we have to compare the obtained solution to the given options.
On considering the given question we have
$$ \Rightarrow {\left( 3 \right)^{\dfrac{1}{4}}}$$ ---- (1)
As we know that the square root of a natural number is a value, which can be written in the form of $$y = \sqrt a = {a^{\dfrac{1}{2}}}$$. It means ‘y’ is equal to the square root of a, where ‘a’ is any natural number.
Similarly, the cube root of a natural number can be written as $$y = \root 3 \of a = {a^{\dfrac{1}{3}}}$$.
On the same way equation (1) can be written as
$$\therefore \,\,\,\,\root 4 \of 3 $$
Hence, the simplest form of $${\left( 3 \right)^{\dfrac{1}{4}}} \to \root 4 \of 3 $$.

Note:
Remember, 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. For the exponential numbers we have a law of indices and by applying it we can solve the given number.