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Roots of Numbers

Roots of Numbers. We are learning to…predict square roots to the nearest tenth and find the principle root of numbers. Saturday, June 7, 2014. Fill in your name, date, period, and learning target…then try the warm up questions and put your pencil down!. Roots of Numbers.

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Roots of Numbers

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  1. Roots of Numbers We are learning to…predict square roots to the nearest tenth and find the principle root of numbers. Saturday, June 7, 2014 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: = ____ Because…42 or (4)(4) =16. What multiplied by itself is 16? = ____ Because…102 or (10)(10) =100. What multiplied by itself is 100?

  4. Examples: = ____ Because…122 or (12)(12) =144. What multiplied by itself is 144? = ____ Because…202 or (20)(20) =400. What multiplied by itself is 400?

  5. Examples: = ____ Because…152 or (15)(15) =225. What multiplied by itself is 225? = ____ Because…1002 or (100)(100) =10,000. What multiplied by itself is 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: The perfect square below 20 is… The perfect square above 20 is… Difference of 4 Difference of 5 No whole number times itself equals 20 but… The solution must be between 4 and 5…but which is the solution closer to? 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: The perfect square below 84 is… The perfect square above 84 is… Difference of 3 Difference of 16 No whole number times itself equals 84 but… The solution must be between 9 and 10…but which is the solution closer to? 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,

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