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Simplifying Radicals

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Simplifying Radicals

Definitely radical, debatably simple.

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.

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

So how do we simplify and … ?

Let’s start with .

Check with a calculator: and

Now let’s try .

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 =12.5

50/9 = 5.555

50/16 = 3.125

50/25 = 2

So50 = 25 x 2

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”

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.

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… ?

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 =

Let’s try two problems…

HW: P 355 (1-23 odd)

Work on this assignment in pairs for the remainder of class.