Chapter 8, Problem 1CT

Write $\sqrt{-12}$ in terms of i.

To determine

To write:

Given expression in terms of $i$.

Answer to Problem 1CT

$\sqrt{-12}$$=$$\boxed{2i\sqrt{3}}$

Explanation of Solution

Given information:

$\sqrt{-12}$

Concept Involved:

The number $i$, called the imaginary unit, is such that $i^2=-1$. (That is, $i$ imaginary unit is the number whose square is -1)

Calculation:

Steps	Description
$\sqrt{-12}$	Given expression
$\sqrt{-1}\cdot \sqrt{12}=\sqrt{-1}\cdot \sqrt{4}\cdot \sqrt{3}=2i\sqrt{3}$	Rewrite, simplify and replace $\sqrt{-1}$ with $i$

Conclusion:

The given expression $\sqrt{-12}$ can be written as $\boxed{2i\sqrt{3}}$