09.22.2018: One Lesson of Math

Today's soundtrack is Amorphis: Queen of Time, an album that filled me with happiness right from the first awesome riff.

This morning, I'm bypassing the Randomizer's activity for the sake of finishing my "Pre-Calculus 11 Introduction Assignment." In this final section, I'll be revisiting radicals.

Simplifying Radicals

To simplify a radical, we convert an entire radical to a mixed radical. We need to remember the following property of radicals: √a x b = √a x √b. We can use this rule to simplify a radical thus: if we have a radical that is being squared and it is the product of two factors, one of which is a perfect square, we can use the square root of the perfect square multiplied by the other factor, then rooted and put outside of the radical symbol, to simplify the radical.

Converting Mixed Radicals to Entire Radicals

If we want to convert a mixed radical (ab), we need to exponentially calculate the coefficient by the index, then we put it inside a radical symbol with the same index as our other radicand, and multiply the two numbers. This gives us our entire radical.