1. Roots of Numbers We are learning to…predict square roots to the nearest tenth and find the principle root of numbers. Monday, November 23, 2015 Fill in your name, date, period, and learning target…then try the warm up questions and put your pencil down!

2. Roots of Numbers  Square Root – A number when multiplied by itself (squared) produces the given number. The opposite or inverse of using an exponent of 2.  The symbol to indicate finding a square root is called a “radical symbol.” It looks like: Your job is to think of the number that when multiplied by itself equals the number inside the radical symbol.

3. Examples: = ____ What multiplied by itself is 16? Because…4 2 or (4)(4) =16. = ____ What multiplied by itself is 100? Because…10 2 or (10)(10) =100.

4. Examples: = ____ What multiplied by itself is 144? Because…12 2 or (12)(12) =144. = ____ What multiplied by itself is 400? Because…20 2 or (20)(20) =400.

5. Examples: = ____ What multiplied by itself is 225? Because…15 2 or (15)(15) =225. = ____ What multiplied by itself is 10,000? Because…100 2 or (100)(100) =10,000.

6. Reflection  Josh believes that. What did Josh do wrong? Help him to correct his error. Remember that does not mean 16 ÷ 2. It means…what number times itself equals or (?)(?) = 16? The correct solution is

7. Predicting square roots of non-perfect squares. Sometimes you will have to find the square root of a number that is not a perfect square…this means that you solution will not be a whole number. For example: No whole number times itself equals 20 but… The perfect square below 20 is… The perfect square above 20 is… The solution must be between 4 and 5…but which is the solution closer to? Difference of 4 Difference of 5 Prediction:__________ (Check with your calculator)

8. Predicting square roots of non-perfect squares. Sometimes you will have to find the square root of a number that is not a perfect square…this means that you solution will not be a whole number. For example: No whole number times itself equals 84 but… The perfect square below 84 is… The perfect square above 84 is… The solution must be between 9 and 10…but which is the solution closer to? Difference of 3 Difference of 16 Prediction:__________ (Check with your calculator)

9. Predicting square roots of non-perfect squares.  Predict the square root of 12 with your group. When you are done check the prediction on your calculator.

10. Negative Roots of Numbers  For every square root there are actually 2 solutions. This because... (Negative Number) (Negative Number) = A Positive Number  For Example: (5)(5) = 25 and also (-5)(-5) = 25 So…  When you see the “radical symbol” just assume you are taking the “principle square root.” (POSTIVE SQUARE ROOT)  If you see negative outside of a radical you are finding the NEGATIVE SQUARE ROOT.

11. Extension:  What do you think means? What is the solution? is asking you to find ? 3 =8 or (?)(?)(?) = 8. Since (2)(2)(2) = 8,