Simplifying Radicals Definitely radical, debatably simple.

Simplifying Radicals So What is a Radical…? A Radical is nothing more than a square root sign EXAMPLES: The expression is read as “radical 20” and The expression is read as “ 5 radical 3.

Simplifying Radicals There are some radicals easy to simplify… For Example: and Other radicals take more work… Like: and … neither has an easy answer, but both can be simplified

Simplifying Radicals So how do we simplify and … ? Let’s start with. Check with a calculator: and Now let’s try.

Simplifying Radicals So what are the rules? What steps can I follow? Step 1: Either know or have a list of your perfect squares present. 4,9,16,25,36,49,64,81,100… These are the numbers that have nice sqrts. Step 2: Determine if any of the square roots divide into your radical evenly. Let’s try : 50/4 = /9 = /16 = /25 = 2 So 50 = 25 x 2

Simplifying Radicals Step 3: Rewrite the radical as the product of two parts. Step 4: Replace the radical that has a perfect square root with a regular number. The answer is read “5 times the square root of 2” or “5 radical 2”

Simplifying Radicals The are other ways to simplify as well… Sometimes we can just use multiplication and division. For Example: and There are also some radicals that cannot be simplified… cannot be broken into two parts.

Simplifying Radicals There is one final method of simplification that we must consider. We are allowed to multiply two radicals or divide two radicals, BUT you cannot divide a regular number by a radical. Example: So what to we do… ?

Simplifying Radicals We have to “rationalize the denominator”… Step 1: Multiply the top and bottom of the fraction by the bottom. Step 2: Simplify Step 1 These =

Simplifying Radicals Let’s try two problems…

Simplifying Radicals HW: P 355 (1-23 odd) Work on this assignment in pairs for the remainder of class.