Question

How do you write $5{{x}^{\dfrac{5}{2}}}$ as a radical form?

Answer 1

Hint: In this question, we have to find the radical form of the expression. Thus, we will use the basic mathematical rule and the square root rule to get the solution. As we know, radical means changing the variable or the number into square root form, that is $\sqrt{{}}$ . Thus, in this problem, we will first split $\dfrac{5}{2}$ as the multiplication of 5 and $\dfrac{1}{2}$ , then we will put the square root in place of $\dfrac{1}{2}$ power so that the power $\dfrac{1}{2}$ will remove. Then, we will take ${{x}^{4}}$ common from the square root to get more simplified $\sqrt{{{x}^{5}}}$ value, and thus get the required solution for the problem.

Complete step by step answer:
According to the problem, we have to get the radical form from the given expression.
Thus, we will use the square root rule and the basic mathematical rule to get the solution.
The expression given to us is $5{{x}^{\dfrac{5}{2}}}$ ------------ (1)
Let us first rewrite $\dfrac{5}{2}$ as the multiplication of 5 and $\dfrac{1}{2}$ , thus we get
$\Rightarrow 5{{x}^{5\times \dfrac{1}{2}}}$
Now, we will remove $\dfrac{1}{2}$ in power, by putting square root symbol, that is $\sqrt{{}}$ outside ${{x}^{5}}$ , thus we get
$\Rightarrow 5\sqrt{{{x}^{5}}}$
Now, we will again simplify the square root by taking ${{x}^{4}}$ out from the square root, because ${{x}^{4}}$ can be written as $x\times x\times x\times x$ . Therefore, we will make the group of two of the multiplication of x’s , we get
$\underline{x\times x}\times \underline{x\times x}$
Thus, when we take ${{x}^{4}}$from the square root, we get two x from the same, therefore we get
$\Rightarrow 5{{x}^{2}}\sqrt{x}$ which is the required solution.
Therefore, for the expression $5{{x}^{\dfrac{5}{2}}}$ , its radical form is equal to $5{{x}^{2}}\sqrt{x}$

Note:
While solving this problem, do mention all the steps carefully to avoid confusion. You can also end your answer after this $5\sqrt{{{x}^{5}}}$ step. Do not forget to mention the definition of radical form, as the solution must contain a square root symbol.