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Concept Square Root

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					                                                            Exponents Outline for Topic 5: Square Root




Concept: Square Root
                                                                      Name:
Warm Up

1. Multiply the following:



     (a) 22 =                       (b) 32 =                          (c) 42 =


     (d) 52 =                       (e) 62 =                          (f) 72 ==




COMPUTER COMPONENT

    Instructions: Select the computer program Understanding Exponents (Neufeld)
                  Follow the instructions to the Main Menu.
                  Select Square Root from the Main Menu.

                  Work through all sections of this topic in order:
                  • Squaring Numbers
                  • Square Roots
                  • Radical Signs
                  • Square Roots of Negative Numbers
                  • Examples Questions
                  • Estimating Square Roots
                  • Estimating Square Roots on a Number Line
                  • Practice Questions

     Additional Required Materials: Scientific calculator


                   As you work through the computer exercises, make your notes in the
                   NOTES section of this page.

                When you reach the end of the section Practice Questions on the computer,
                move on to the OFF COMPUTER EXERCISES below.



              Neufeld Learning Systems Inc. 2008
              www.neufeldmath.com                                                          1
                                                               Exponents Outline for Topic 5: Square Root


NOTES

Squaring Numbers

                      A number is squared when it is ____________________ by _____________.


Fill in the following examples of squares.


                      12        =           1       1      =               1


                      22        =       ____        ____   =           _______


                  (-2)2         =       ____        ____   =           _______


                      72        =       ____        ____   =           _______


                  (-7)2         =       ____        ____   =           _______


                  4.52          =       ____        ____   =           _______


                 (-4.5)2        =       ____        ____   =           _______


                      a2        =       ____        ____   =           _______


                  (-a)2         =       ____        ____   =           _______



Fill in the blanks.

           (a) Every positive number has ____ square roots; one _____________________

               and one _______________________________.


                           Example:

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               www.neufeldmath.com                                                            2
                                                                  Exponents Outline for Topic 5: Square Root




                                22    =     2        ______     = ______

                             (-2)2    = ( -2 )       ( ____ )   = _____

                            The square roots of __________ are ________ and _______ .


          (b) The                    symbol is called a ___________________ sign.


          (c) The radical sign tells you to take the______________________ square root.



What number has been squared to get the number under the square root symbol?


          (a)          64



          (b)          25


A number cannot be _____________________ by __________________ to give a

__________________ product.



                Example:              -4                          2       2   =    4

                                                                 -2     -2 =       4




                                          The product is always a __________________ number.


      We ______________________ take the square root of a _______________________ number.



                Neufeld Learning Systems Inc. 2008
                www.neufeldmath.com                                                              3
                                                                      Exponents Outline for Topic 5: Square Root


Remember:

            Operations ______________ the _________________ sign are done _________.

                      Example:


                              4 + 10           =
                                                         ________


                                               =       ________


            A square root can be written as a __________ of two radicals.


                      Example:


                      (a)        6                 =         2     3


                                               =       ___       ___


                      (b)       9              =             3    3


                                                                      ---
                                               =       ( )
                                                         ___


When estimating square roots.

            First, find an easier square root that is close, but a little _____________than it.

            Then find an easier square root that is just a little ____________ than it.

                      Example:


                      (a)     28       is ____________                       and




              Neufeld Learning Systems Inc. 2008
              www.neufeldmath.com                                                                    4
                                                               Exponents Outline for Topic 5: Square Root


OFF COMPUTER EXERCISES

1. Find the square roots of each number.

   (a)    81                                         (b) 64




   (c)    1                                          (d) 0




   (e)    100                                        (f) 144




   (g)    9                                          (h) 225




2. Which square roots are the following between?


         (a)            72




         (b)            38




         (c)            109




                Neufeld Learning Systems Inc. 2008
                www.neufeldmath.com                                                           5
                                                            Exponents Outline for Topic 5: Square Root


3. Fill in the missing numbers on the radical clock face:




4. Evaluate.




           (b)              -




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                 www.neufeldmath.com                                                       6
                                           Exponents Outline for Topic 5: Square Root



(c)




(d)                 -




(e)             +




(g)




(h)




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      www.neufeldmath.com                                                 7
                                           Exponents Outline for Topic 5: Square Root




(i)




(j)




(k)




(l) 4 +




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      www.neufeldmath.com                                                 8
                                                                  Exponents Outline for Topic 5: Square Root


5. Evaluate each expression if        x = 3,         y = -4 and     z = -7.

          (a)       -




          (b)




          (c)




          (d)




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                www.neufeldmath.com                                                              9
                                                            Exponents Outline for Topic 5: Square Root




6.   Answer the following and show all your steps.

           (a) If the area of a square is 289 square mm, calculate the dimensions.




          (b) If the area of a square is 0.0081 square cm, calculate the dimensions.




          (c) A rectangle has dimensions of 4 cm by 16 cm and is equal to a second figure
              which is a square. Find the dimensions of the square.




              Neufeld Learning Systems Inc. 2008
              www.neufeldmath.com                                                          10
                                                          Exponents Outline for Topic 5: Square Root


Challenge


   6. Calculate the square root of (43 + 43 + 43 + 43).




   7.   Find a number x to make this statement true:

              4 + ( x ÷ 42) – 2        32 = 18




               Neufeld Learning Systems Inc. 2008
               www.neufeldmath.com                                                       11

				
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