Question

How do you write the expression ${m^{ - \dfrac{1}{2}}}$ in radical form?

Answer 1

In this question, we have to find out the required expression from the given particulars.
We need to first understand the meaning of a radical symbol.
Radical:
The √ symbol that is used to denote square root of nth roots
Radical expression:
A radical expression is an expression containing a square root.
We need to convert the expression into a form which contains square root, after converting it we can find out the required solution.

Formula used: Index formula:
i) ${x^{\dfrac{1}{n}}} = \sqrt[n]{x}$
ii) ${x^{ - m}} = \dfrac{1}{{{x^m}}}$

Complete step-by-step solution:
We need to write the expression ${m^{ - \dfrac{1}{2}}}$ in radical form.
Since, Radical symbol is √ which is used to denote square root of nth roots and a radical expression is an expression containing a square root, we need to convert the given expression in a square root form.
Using the formula ${x^{ - m}} = \dfrac{1}{{{x^m}}}$ in given expression we get,
${m^{ - \dfrac{1}{2}}} = \dfrac{1}{{{m^{\dfrac{1}{2}}}}}$
Again using the formula ${x^{\dfrac{1}{n}}} = \sqrt[n]{x}$ in the denominator we get,
${m^{ - \dfrac{1}{2}}} = \dfrac{1}{{{m^{\dfrac{1}{2}}}}} = \dfrac{1}{{\sqrt m }}$, which is the required radical form.

Hence, the expression ${m^{ - \dfrac{1}{2}}}$ in radical form is $\dfrac{1}{{\sqrt m }}$.

Note: Radical symbol:
A radical is a symbol that represents a particular root of a number. This symbol is shown below.
√
Although this symbol looks similar to what is used in long division, a radical is different and has a vastly different meaning. The radical, by itself, signifies a square root. The square root of a number n is written as follows.$\sqrt n$.
Radical expression:
A radical expression is an expression containing a square root.