Question

How do you write ${x^{\dfrac{3}{4}}}$ in radical form?

Answer 1

Hint: To solve this question, we first need to understand what the radical form is. A Radical is defined as an expression that involves a root, usually a square root or cube root. There are three elements of a radical form: radicant, radical symbol and degree. We will first discuss these elements and then by the help of it, we will reach our required answer.

Complete step-by-step answer:
We will first discuss the elements of a radical form.
First is the radicant. The radicant is the one of which we are finding the root. A radical equation is the one that has at least one variable expression within a radical, most often the square root. This radical can be any root, maybe square root, cube root. Generally, we can solve equations by isolating the variable by undoing what has been done to it.
The symbol of ‘root of’ which is \[\sqrt {} \]is taken as the radical symbol.
Third element is the degree. The degree indicates the number of times a radicand is multiplied by itself. If there is no number on the root symbol, it is assumed as 2 which is known as the square root.
Now we will convert the given term in the radical form.
We have ${x^{\dfrac{3}{4}}}$.
It can be rewritten as
${x^{\dfrac{3}{4}}} = {\left( {{x^3}} \right)^{\dfrac{1}{4}}} = \sqrt[4]{{{x^3}}}$

Thus, the radical form of ${x^{\dfrac{3}{4}}}$ is $\sqrt[4]{{{x^3}}}$

Note: In this question, we have discussed the components of radical forms and then converted the given number to its radical form. Let us now see the components of our final answer.
Our final answer is: $\sqrt[4]{{{x^3}}}$
Radicant: ${x^3}$
Radical symbol: \[\sqrt {} \]
Degree: 4