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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.

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simplifying radicals

Simplifying Radicals

Definitely radical, debatably simple.

simplifying radicals1
Simplifying Radicals

So What is a Radical…?

A Radical is nothing more than a square root sign


The expression is read as “radical 20” and

The expression is read as “ 5 radical 3.

simplifying radicals2
Simplifying Radicals

There are some radicals easy to simplify…

For Example:


Other radicals take more work…


and … neither has an easy

answer, but both can be simplified

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Simplifying Radicals

So how do we simplify and … ?

Let’s start with .

Check with a calculator: and

Now let’s try .

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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 =12.5

50/9 = 5.555

50/16 = 3.125

50/25 = 2

So50 = 25 x 2

simplifying radicals5
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 radicals6
Simplifying Radicals

The are other ways to simplify as well… Sometimes we can just use multiplication and division.

For Example:


There are also some radicals that cannot be simplified…

cannot be broken into two parts.

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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.


So what to we do… ?

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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 =

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Simplifying Radicals

Let’s try two problems…

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Simplifying Radicals

HW: P 355 (1-23 odd)

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