Question

How do you simplify $-{{9}^{\dfrac{1}{2}}}$ ?

Answer 1

Hint: In this question we are asked to simplify the given number. For doing that we will use basic arithmetic simplification techniques and reduce it into a simple number. From the basic concept of complex numbers we know that $i=\sqrt{-1}$ we will use this to simplify this.

Complete step by step solution:
Here we have been asked to simplify the given number $-{{9}^{\dfrac{1}{2}}}$ .
For solving this question we will use basic arithmetic simplification techniques and reduce it into a simple number.
From the basics of concepts of complex numbers we know that there exists an imaginary number known as iota given as $i=\sqrt{-1}$ .
We can use this value in our solution to simplify this given number.
We will write the exponent fractional power as square root. After that we will have
$-{{9}^{\dfrac{1}{2}}}=\sqrt{-9}$.
Now we will use the concept of iota after applying that we will have $\Rightarrow \sqrt{-9}=i\sqrt{9}$ .
As we know that we can express the number nine as a square of 3 we will do that here.
 After using this here we will have $\Rightarrow i\sqrt{9}=i\sqrt{{{3}^{2}}}$ .
Now we will remove the square root over the number three square. And after removing that we will have $\Rightarrow i\sqrt{{{3}^{2}}}=3i$ .

Therefore we can conclude that the given number can be simply expressed as $-{{9}^{\dfrac{1}{2}}}=3i$

Note: In questions of this type during solving we should take care of the mistakes which we make. This is a very simple question and can be easily answered within a short span of time without using a pen and paper. Here someone can misunderstand the question and solve it as $-{{9}^{\dfrac{1}{2}}}=-\left( {{9}^{\dfrac{1}{2}}} \right)\Rightarrow -\sqrt{9}\Rightarrow -\sqrt{{{3}^{2}}}=-3$ it’s a clear wrong assumption.