Question

$\sqrt{12 + \sqrt{ - 9} }$write as a complex number

Answer 1

A complex number is of the form a+bi, where

$i=\sqrt[]{-1}$

Given data:

We are given the folowing complex number

$\sqrt[]{12}+\sqrt[]{-9}$

Now,let us solve the square roots to write the number in standard form,

$\sqrt[]{12}=\sqrt[]{2\times2\times3}=2\sqrt[]{3}$

Also,

$\begin{gathered} \sqrt[]{-9}=\sqrt[]{9}\times\sqrt[]{-1} \\ =3i \end{gathered}$

So, the complex number will be

$\sqrt[]{12}+\sqrt[]{-9}=2\sqrt[]{3}+3i$

So, the correct option is D).