Irrationalizingism numberismsssssss 2.ppt

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Square Roots and IrrationalNumbers

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Squares and Roots 2 2 2 2 2 2 2 2 2 2 2 2 11 2 4 3 9 4 16 5 25 6 36 7 49 8 64 9 81 10 100 11 121 12 144             1 1 4 2 9 3 16 4 25 5 36 6 49 7 64 8 81 9 100 10 121 11 144 12            

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Note!!! Notice that squaresand square roots are inverses (opposites) of each other.

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Estimating Square Roots Onceyou memorized squares and their roots, we can estimate square roots that are not perfect squares  For example, what about 8

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Estimating Square Roots We find the two perfect squares that are before and after the square root of 8. . .  and  Look at them on a number line: 4 9 5 4 9 6 7 8 3 2 2 3

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Estimating square roots We can see that is between 2 and 3 but is closer to 3. We would say that is approximately 3. 4 5 9 6 7 8 3 2 2 3 8 8

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TRY THIS: Estimate tothe nearest whole number 27 78  50 Click to the next slide to see if you are right!

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TRY THIS: Estimate tothe nearest whole number 27 78  50 5 -9 7

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 Rational number-can be written as a fraction  Irrational number- cannot be written as a fraction because: •it is a non-terminating decimal •it is a decimal that does NOT repeat * The square roots of ALL perfect squares are rational. * The square roots of numbers that are NOT perfect squares are irrational.

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Try This: Identifyeach number as rational or irrational 2 81  0.53 0.627 13.875931...

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Identify each numberas rational or irrational. 2 81  0.53 0.627 13.875931... Irrational Rational Rational Rational Irrational

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Irrationalizingism numberismsssssss 2.ppt

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