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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”

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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.