Radicals Simplifying Square Root Expressions

This section has the following videos:

  • Lesson Video
  • Example Set A Practice Problems (Video Solutions)
  • Example Set B Practice Problems (Video Solutions)
  • Example Set C Practice Problems (Video Solutions)

Ah…the wonderful world of the radical (square root symbol).  Don’t like radicals? Too bad- they are everywhere in algebra and math so chill out and get to love these little rascals.   The first order of business when dealing with radicals is being able to simplifying them.  Just like “simplifying” fractions (reducing  ex.  20 / 40 simplified to 1 / 2) when we simplify a radical expression we want to write it as simple as possible. The key to simplifying a radical is to look for perfect square factors these are numbers with nice, friendly whole number square roots – examples are 4, 9, 16, 36, 100.   Next we need to understand a cool property about radicals which is we can write a radical as the product of it’s factors.  As you can see from the steps below the key to simplifying radicals is to hunt down these perfect square factors and rewrite the radical as the product of it’s factors (one or more being a perfect square).  One last point- put away your calculator. Knowing that the square root of 75 is 8.66025.. is not the type of simplifying we are doing here just wanted to stress this just in case you were tempted to take the easy way out.  You’re way smarter than that calculator!