Question

How do you write the expression \[{2^{\dfrac{1}{6}}}\] in radical form?

Answer 1

Hint:
In the given question, we have been asked to find the radical form of an even natural number. To solve this question, we must know the meaning of radical form. Radical form means the square root of the number. If the number is a perfect square, then it is having no integer left in the square root. But if it is not a perfect square, then it has at least one integer in the square root.

Complete step by step answer:
The given number whose radical form is to be found is \[{\left( 2 \right)^{\dfrac{1}{6}}}\].
A radical form of a number means its square root.
So, we have to find the simplified form of \[{\left( 2 \right)^{\dfrac{1}{6}}}\].
The number in the denominator of the power is the “$n^{th}$” root.
It means that the number is placed inside the root bracket, with the number in the denominator written in the little place of the outside of the bracket.
Hence, \[{\left( 2 \right)^{\dfrac{1}{6}}} = \sqrt[6]{2}\]

Thus, the simplified radical form of \[{2^{\dfrac{1}{6}}}\] is \[\sqrt[6]{2}\].

Note:
So, for solving questions of such type, we first write what has been given to us. Then we write down what we have to find. Then we write the formula which connects the two things. When we are calculating such questions, we find the prime factorization, club the pairs together, take them out as a single number and solve for it. This requires no further action or steps to evaluate the answer.