\sqrt{12 + √( - 9) }write as a complex number

Question

`\sqrt{12 + √( - 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*2*3}=2\sqrt[]{3}`

Also,

`\begin{gathered} \sqrt[]{-9}=\sqrt[]{9}*\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).