Question

Sqrt(-28)write in terms of i

Answer 1

`\sqrt[]{-28}=2\sqrt[]{7}i`

Step-by-step explanation:

The square roots of negative numbers do not exist on the number line.

This is the reason why there exist, Complex Numbers.

Under this, we have the definition:

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

Given

`\sqrt[]{-28}`

We can rewrite this as:

`\begin{gathered} \sqrt[]{-1*28} \\ OR \\ \sqrt[]{-1}*\sqrt[]{28} \\ =\sqrt[]{-1}*\sqrt[]{4*7} \\ \\ =\sqrt[]{-1}*\sqrt[]{4}*\sqrt[]{7} \\ =i*2*\sqrt[]{7} \\ \\ =2\sqrt[]{7}i \end{gathered}`