1. Rationalize Non-Perfect Squares

2. What is a square root? 5 and 5 Two identical factors of a number.
What if it is a Non-Perfect Square????
You can approximate to a decimal
Or you can simplify the answer with a method called Rationalizing (or ‘extracting perfect squares’)
5 and 5

3. Perfect Squares: KNOW 1-20 and their square roots.
1,4,9,16,25,36,49,64,81,100,
121, 144,169,196,225,256,289,324, 361,400

4. Rationalizing = extracting perfect squares
We are going to “simplify” the radical (square root #) as much as possible.
Break the number into its “perfect square” factors and simplify those, leave the non-perfect factors inside the radical
Find
List the factors of 20: 1· 20, 2· 10, 4· 5
Select the factors 4 and 5 because 4 is the only perfect square factor of 20
Break 20 up into the factors, simplify the perfect square

5. Prove that this is true…
2 • 2 = 4
4 • 5 = 20

6. Find the This is not a perfect square.
Think of all the perfect square factors:
16 times 3
4 times 12
The BEST perfect square factor is 16 because it is largest

7. Find the This is not a perfect square.
Think of all the perfect square factors:
100 times 2
25 times 8
The BEST perfect square factor is 100 because it is largest

8. Find the What if you used 25 times 8 instead of 100 times 2?
It’s ok!! You will just have to rationalize again, like reducing a fraction twice
Now notice 8 still has perfect square factors, so rationalize 8

9. Rationalize the following: