Question

compare and contrast the difference between simplify a fraction and simplify a radical. What is the ultimate goal for each?

Answer 1

Compare:
- The goal of reducing a radical and a fraction is to literally simplify the numbers to make them easier to work with

Contrast:
- The action of simplifying fractions is dividing the numerator and denominator by a common factor. 
- The action of simplifying radicals is making sure the radicand has no square factors. You separate the radicand into two parts, one of which can be square rooted into a whole number.
Example:
$\sqrt{18} = \sqrt{9} * \sqrt{2} = 3 \sqrt{2}$