Simplify square roots of negative numbers

The  exercise appears under the Algebra II Math Mission. This exercise practices rewriting square roots of negative numbers as imaginary numbers.

Types of Problems
There is one type of problem in this exercise:


 * 1) Express the radical using the imaginary unit, $$i$$.: This problem asks for the radical of a given number. The student is expected to find the square root and express it as an imaginary number.Simplify square roots of negative numbers.PNG

Strategies
Knowledge of imaginary numbers are needed for this exercise.
 * 1) The imaginary unit $$i$$ is defined as $$\sqrt{-1}$$ So for any negative real number $$-a$$, students can express $$\sqrt{-a}$$ as $$i\sqrt{a}$$.
 * 2) The square root of a negative number is imaginary, because a negative multiplied by a negative always equals a positive number. (example: $$\sqrt{-16} = 4i$$)

Real-life applications

 * 1) Square roots have many uses in the physics as they are the way to undo squares in famous formulas like $$E=mc^2$$.
 * 2) Applications to trigonometry are also evident since the right triangle trigonometry is based on the Pythagorean Theorem.
 * 3) In geometry, the square root is necessary to find the distance between points or the magnitude of a vector.