Simplify Radicals

Simplify Radicals

What is a radical?

• Another name for a square root

Radical:

This is read as "radical 17"

Simplify "PERFECT" square  roots

A radical is considered a perfect square root IF when put in a calculator, it does not give you a decimal answer. (exceptions: see fraction slide)

Think of it  (sorta) as the opposite of squaring a number

Examples:

Using a calculator makes this easy

Answer is:

9

Some of them we know by heart.

Actually, it would be in your best interest to MEMORIZE the first 
15 perfect squares.
In other words, 1x1 = 1
2x2=4, 3x3=9,   4x4 = 16
 until you get to 15x15 =225

This way

You won't need a calculator to figure the square roots of those.
You will already know them.

Fractions

So, I told you about an exception.
What if you had this --->

All you do  is 

Separate it into a radical divided by a radical and solve for the radicals

Practice by completing the first half of your assignment

There are 10 problems.  Do those now. Then move to the next slide

Write your first 10 perfect squares

 for example, the first three are 1, 4, 9...
you fill out the other 7 on your paper

If your radical is NOT a perfect square

Here is how you simplify them:

Factor Tree method

Factor

What numbers multiply to equal 50?
I chose 5x10

5 is prime but 10 is not. So I have to continue until all numbers (ends of the branches) are prime.

If there are pairs,

Circle them.
The square root of 5x5(25) is 5
That number goes outside the radical

Single numbers

Stay under the radical.
if there is more than one, multiply them together and put under radical.

Here is a more involved example

The prime numbers we have are 3,3,2,5.
The 3 will go to the outside of radical.  The leftover 2 & 5 will be multiplied and left under the radical.

Now for practice

Go to your worksheet.  There is plenty of practice.  Ask questions to make sure you understand.