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1.2 Square Roots of Non-Perfect Squares

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					1.2 Square Roots of
Non-Perfect Squares
      Math 90
           Introduction...
• Many fractions and decimals are not
  perfect squares.
• A fraction or decimal that is not a
  perfect square is called a non-perfect
  square.
  – The square roots of these numbers do not
    work out evenly!
• How can we estimate a square root of a
  decimal that is a non-perfect square?
              Here are 2 strategies...
Ask yourself: “Which 2
 perfect squares are                7.5
   closest to 7.5?”
                                   7.5




                 2           2.5           3

7.5 is closer to 9 than to 4, so 7.5 is closer to 3 than to 2.
          What would be a good approximation?
           Strategy #2...
• Use a calculator! 
• But, of course, you must be able to do
  both!
           Example #1
• Determine an approximate value of
  each square root.
   8      close to 9    We call these 2
                           numbers
   5      close to 4    „benchmarks‟.

                 8 3
                  
                 5 2

            What does this
              mean?
               Example #2
• Determine an approximate value of
  each square root.
                          Your
    3
                0.3   benchmarks!
   10


        0.20   0.25     0.30     0.36 0.40

     3                 Of course, you can always
        0.55          use a calculator to CHECK
    10                        your answer!
       What‟s the number?
• Identify a decimal that has a square root
  between 10 and 11.

      If these are the square
     roots, where do we start?
                                 121

       100             110       120




         10                       11
                    Mr. Pythagoras

           • Junior High Math Applet




Remember, we
 can only use
 Pythagorean
 Theorem on
 RIGHT angle
   triangles!
       Practicing the Pythagorean
                Theorem
       First, ESTIMATE each missing side and then
               CHECK using your calculator.


                                                  7 cm

                 x                  13 cm
5 cm


          8 cm
                                              x
Applying the Pythagorean
        Theorem

                                 1.5 cm
   2.2 cm
                    6.5 cm

 The sloping face of this ramp needs to be
          covered with Astroturf.

a) Estimate the length of the ramp to the
   nearest 10th of a metre

b) Use a calculator to check your answer.

c) Calculate the area of Astroturf needed.
  Let‟s quickly review what
   we‟ve learned today...

• Explain the term non-perfect square.
• Name 3 perfect squares and 3 non-
  perfect squares between the numbers 0
  and 10.
• Why might the square root shown on a
  calculator be an approximation?
            Assignment Time!
•   Complete the following questions in your notebook.
•   Be prepared to discuss your answers in class.
•   Show all of your work!
•   Write this assigned questions on your assignment
    sheet:
     – Pg. 18/19: 4ae, 5ab, 6ab, 7bc, 8ab, 9ab, 10ac,
       11bef, 13ac

				
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