Estimating Square Roots by ferda.gurcan

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									 4-6 Estimating Square Roots
  4-6 Estimating Square Roots




               Warm Up
               Problem of the Day
               Lesson Presentation




 Course
Course 3 3
 4-6 Estimating Square Roots

     Warm Up
     Find the two square roots of each
     number.
     1. 144     12        2. 256        16


     Evaluate each expression.
     3. 8+ 144 20           4. 7   289   119




Course 3
 4-6 Estimating Square Roots


     Problem of the Day
     A pyramid of blocks is built in layers. The
     bottom layer has 62, or 36, blocks. The
     next layer has 52 blocks, and so on until
     the top layer has 1 block. How many
     blocks are there in all?
      91 blocks




Course 3
 4-6 Estimating Square Roots



      Learn to estimate square roots to a given
      number of decimal places and solve
      problems using square roots.




Course 3
 4-6 Estimating Square Roots
 Additional Example 1A: Estimating Square Roots of
                     Numbers
     Each square root is between two integers.
     Name the integers. Explain your answer.
                     Think: What are perfect
           55        squares close to 55?
     72 = 49         49 < 55

     82 = 64         64 > 55

           55 is between 7 and 8 because 55 is
           between 49 and 64.


Course 3
 4-6 Estimating Square Roots
 Additional Example 1B: Estimating Square Roots of
                Numbers Continued
     Each square root is between two integers.
     Name the integers. Explain your answer.
                 Think: What are perfect
      – 90
                 squares close to 90?
       –92 = 81   81 < 90

     –102 = 100   100 > 90

    – 90 is between –9 and –10 because 90 is
        between 81 and 100.



Course 3
 4-6 Estimating Square Roots
                   Check It Out: Example 1A

     Each square root is between two integers.
     Name the integers. Explain your answer.
                     Think: What are perfect
           80
                     squares close to 80?
     82 = 64         64 < 80

     92 = 81         81 > 80

            80 is between 8 and 9 because 80 is
            between 64 and 81.



Course 3
 4-6 Estimating Square Roots
                Check It Out: Example 1B

     Each square root is between two integers.
     Name the integers.
                  Think: What are perfect
       – 45
                  squares close to 45?
     –62 = 36     36 < 45

     –72 = 49     49 > 45

    – 45 is between –6 and –7 because 45 is
         between 36 and 49.



Course 3
 4-6 Estimating Square Roots
Additional Example 2: Problem Solving Application

           You want to sew a fringe on a square
           tablecloth with an area of 500 square
           inches. Calculate the length of each side of
           the tablecloth and the length of fringe you
           will need to the nearest tenth of an inch.

           Understand the Problem
           First find the length of a side. Then you can
           use the length of a side to find the
           perimeter, the length of fringe around the
           tablecloth.

Course 3
 4-6 Estimating Square Roots
              Additional Example 2 Continued

           Make a Plan
           The length of a side, in feet, is the number
           that you multiply by itself to get 500. To be
           accurate, find this number to the nearest
           tenth. If you do not know a step-by-step
           method for finding 500, use guess and
           check.




Course 3
 4-6 Estimating Square Roots
                   Additional Example 2 Continued
      Solve
   Because 500 is between 222 and 232, the square root
   of 500 is between 22 and 23.

            Guess 22.5             Guess 22.2        Guess 22.4           Guess 22.3
           22.52 = 506.25     22.22 = 492.84        22.42 = 501.76       22.32 = 497.29
             Too high               Too low           Too high              Too low
           Square root is      Square root is       Square root is       Square root is
            between 22         between 22.2         between 22.2         between 22.3
             and 22.5            and 22.5             and 22.4             and 22.4


                                         2      4       3    1
                            22.0         22.2        22.4         22.6

   The square root is between 22.3 and 22.4.
Course 3
 4-6 Estimating Square Roots
               Additional Example 2 Continued

           Solve

      The square root is between 22.3 and 22.4. To
      round to the nearest tenth, look at the next
      decimal place. Consider 22.35.

       22.352 = 499.5225        Too low
       The square root must be greater than 22.35, so
       round up.
       To the nearest tenth,   500 is about 22.4.
       The length of each side of the table is about
       22.4 in.
Course 3
 4-6 Estimating Square Roots
               Additional Example 2 Continued

           Solve
           The length of a side of the tablecloth is 22.4
           inches, to the nearest tenth of an inch. Now
           estimate the length around the tablecloth.
           4 • 22.4 = 89.6      Perimeter = 4 • side
           You will need about 89.6 inches of fringe.




Course 3
 4-6 Estimating Square Roots
              Additional Example 2 Continued

           Look Back
           The length 90 inches divided by 4 is 22.5
           inches. A 22.5-inch square has an area of
           506.25 square inches, which is close to 500,
           so the answers are reasonable.




Course 3
 4-6 Estimating Square Roots
                 Check It Out: Example 2

           You want to build a fence around a
           square garden that is 250 square feet.
           Calculate the length of one side of the
           garden and the total length of the fence,
           to the nearest tenth.
           Understand the Problem
           First find the length of a side. Then you
           can use the length of a side to find the
           perimeter, the length of the fence.




Course 3
 4-6 Estimating Square Roots
             Check It Out: Example 2 Continued

           Make a Plan
           The length of a side, in feet, is the number
           that you multiply by itself to get 250. To be
           accurate, find this number to the nearest
           tenth. If you do not know a step-by-step
           method for finding 250, use guess and
           check.




Course 3
 4-6 Estimating Square Roots
             Check It Out: Example 2 Continued
           Solve
           Because 250 is between 152 and 162, the square
           root of 250 is between 15 and 16.
              Guess 15.5             Guess 15.9         Guess 15.7           Guess 15.8

             15.52 = 240.25       15.92 = 252.81   15.72 = 246.49           15.82 = 249.46

                Too Low               Too high            Too Low              Too Low

             Square root is       Square root is       Square root is       Square root is
             between 15.5         between 15.5         between 15.7         between 15.8
                and 16              and 15.9             and 15.9             and 15.9


                              1            3       4      2
                              15.5         15.7         15.9         16.1

           The square root is between 15.8 and 15.9.
Course 3
 4-6 Estimating Square Roots
              Check It Out: Example 2 Continued

           Solve

           To round to the nearest tenth, look at the next
           decimal place.
           Consider 15.85.      15.852 = 251.2225
           The square root is lower than 15.85, so round
           down.
           To the nearest tenth, 250 is about 15.8.
           The length of each side of the garden is
           about 15.8 ft.

Course 3
 4-6 Estimating Square Roots
              Check It Out: Example 2 Continued


           Solve
           The length of a side of the garden is 15.8
           feet, to the nearest tenth of a foot. Now
           estimate the length around the garden.

           4 • 15.8 = 63.2      Perimeter = 4 • side

           You will need about 63.2 feet of fence.




Course 3
 4-6 Estimating Square Roots
             Check It Out: Example 2 Continued

           Look Back
           The length 63.2 feet divided by 4 is 15.8
           feet. A 15.8 foot square has an area of
           249.64 square feet, which is close to 250,
           so the answers are reasonable.




Course 3
 4-6 Estimating Square Roots
Additional Example 3: Using a Calculator to Estimate
             the Value of a Square Root

      Use a calculator to find   600. Round to
      the nearest tenth.

     Using a calculator,   600 ≈ 24.49489742….

      Rounded,   600 is 24.5.




Course 3
 4-6 Estimating Square Roots
                 Check It Out: Example 3


      Use a calculator to find   800. Round to
      the nearest tenth.

     Using a calculator,   800 ≈ 28.2842712….

      Rounded,   800 is 28.3.




Course 3
 4-6 Estimating Square Roots
                          Lesson Quiz
      Each square root is between two integers.
      Name the two integers.
      1.   27   5 and 6         2. –    456   –22 and –21


      Use a calculator to find each value. Round
      to the nearest tenth.
      3.   89   9.4             4.     1223   35.0

      5. A square field has an area of 2000 square
      feet. To the nearest foot, how much fencing
      would be needed to enclose the field? 179 ft

Course 3

								
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