Question

How do you change the expression ${{5}^{\dfrac{1}{2}}}$ to radical form?

Answer 1

Hint: Since, the question asks us for the conversion of the given number to a radical one, so for this we will use the correct definition of it and use its sign which is given by $\sqrt{{}}$. With the help of this sign, we will be able to solve the question perfectly.

Complete step by step solution:
To solve this question, we need to first get through the topic of radical form. A radical form is a kind of form in which any number is written along with a square root. We denote the symbol of radical by $\sqrt{{}}$, which is known as a square root. For example, if we take a number 7 and write it in a radical form then we will write it as $\sqrt{7}$.
Now, we will consider the given number to us which is ${{5}^{\dfrac{1}{2}}}$. Since, any number with the power of $\dfrac{1}{2}$ is represented as $\sqrt{{}}$ therefore, the radical form of the given number will be $\sqrt{5}$.
Hence, we can change the number ${{5}^{\dfrac{1}{2}}}$ into a radical form $\sqrt{5}$.

Note: The radical type of number must be converted from a number which has a power of $\dfrac{1}{2}$. This is basically its identification. If we got number 25 instead of 5 then its radical form would be $\sqrt{25}$ which somehow results in 5 only. To get full marks, it is important to write the definition along with any example. Plus one should know the correct sign of the radical. Because if we got a number ${{5}^{\dfrac{1}{3}}}$ then its radical will be $\sqrt{{{5}^{\dfrac{1}{3}}}}$ which is eventually results into ${{5}^{\dfrac{2}{3}}}$. But do not get confused for ${{5}^{\dfrac{2}{3}}}$ as the desired answer because of the fact that this is not represented in a radical form.