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					           Square Roots
        Chapter 9.1 page 453
               What does it mean?
   Before--you found squares of numbers.
Now--you’ll find and approximate square roots of
                    numbers.
     Why!!!!!! So you can solve equations.
           Square Root Websites
• http://www.purplemath.com/modules/radicals.htm
• http://www.aplusmath.com/games/matho/MultMatho.html
• http://www.aplusmath.com/Games/index.html
• http://www.aplusmath.com/Flashcards/sqrt.html
• http://www.aplusmath.com/Flashcards/index.html
• http://www.factmonster.com/ipka/A0875926.html
• Divisibility rules websites
• http://argyll.epsb.ca/jreed/math7/strand1/1104.htm
• http://jc-schools.net/PPT/pfdivisibility.ppt#2
• http://www.nebo.edu/misc/learning_resources/ppt/k-
  5/div_rules.ppt#1
• http://www.lessontutor.com/lw6.html
             Inverse Operations
•   Every operation has an inverse (opposite).
•   Subtraction is the inverse of addition.
•   Division is the inverse of multiplication.
•   Square roots are the inverse of squaring.
•                                    32

• Describe and give an example of a perfect
  square.
     Below is a list of the most common
                     roots.
      SQUARE             CUBE       FOURTH
•   √0 = 0     √49 = 7   ∛0 = 0     4√0 =0
•   √1 = 1     √64 = 8   ∛1 = 1     4√1 = 1

•   √4 = 2     √81 = 9   ∛8 = 2    4√16 = 2

•   √9 = 3    √100 = 10 ∛27 = 3    4√81 = 3

•   √16 = 4   √121 = 11 ∛64 = 4
•   √25 = 5   √144 = 12 ∛125 = 5
•   √36 = 6   √169 = 13
  Every positive number has 2 square
                 roots.
  One is positive and one is negative.
• 4 = 2, because 22 = 4
• However, 4 = -2, because (-2)2 = 4
• The radical sign  , represents a nonnegative
  square root. The symbol , read “plus or
  minus,” refers to both square roots of a positive
  number.
• Because zero is neither positive or negative, it
  has only one square root, 0.
     Find the square roots of the number.
1.    4
2.    16
3.    36
4.    64
5.    121
6.    144
7.    225
8.    256
   You can use perfect squares to
approximate a square root of a number
     that is not a perfect square.
Approximate 51 to the nearest integer
•   Looking at part of our list of square roots:
•    1 = 1
•    4 = 2
•    9 = 3
•    =4
•    =5
•    =6
•    =7
•    =8
       51 is between 49 and 64, and
            closer to 49 than 64.
• Since 49 is 7 and 64 is 8, the 51 is between 7 and
  8.
• 7  51  8
• So approximating 51 to the nearest integer would be
• 7.
• Approximate 125 to the nearest whole number.
• 92 =
• 102 =
• 112 =
• 122 =
  Approximate to the nearest integer.
1. 10

2. -84

3. 151

4. -200
           Solve the equation.
• In September of every even-numbered year,
  people in Marostica, Italy, play an unusual
  chess game. Each chess piece is portrayed by
  a person. The people portraying the knights
  are even on horseback!
• The chessboard is a square with an area of 324
  square meters. What is the length of each side
  of the board? To answer the question, we need
  to know how to find the area of a square.
                     A = s2
• Since we know the area of the chessboard is
  324 m, we substitute that amount into our
  equation.
                      • A = s2
                      • 324 = s2
• To solve it, take the square root of both sides.
                    • 324 = s2
                       • 18 = s
             Solve the equations.
1. a2 = 9

2. n2 = 25

3. 361 = x2

4. 400 = y2
           Radical Expressions
• A radical expression is an expression that
  involves a radical sign. 11 + 52
• 11 + 25 = 36, and 36 = 6
• Always evaluate the expression under the
  radical sign before finding the square root.
• Evaluate 2a + b2, when a = 11 and b = 5.
• Substitute 11 in for a and 5 in for b and solve.
    Evaluate when a = 12 and b = 4.
1. a + b

2. b2 – a

3. 3ab + 1

4. Evaluate when a = 48 and b = 12
   a - b
  An amusement park ride includes a
      free fall drop of 272 feet.
You can use the equation d = 16t2 to determine
  the time t in seconds that it takes a dropped
  object to fall a distance of d feet. How long
  does the free fall part of the ride take?
    d = 16t2                original equation
 272 = 16t2                 substituting 272 for d
   17 = t2                  dividing by 16
17 = t                    taking the square root
 4.1 = t                   Approximating the sq. rt
You can use the following rule of thumb
    when photographing fireworks.
The f-stop, a number that describes the size of
 the opening of the camera lens, should be the
 number closest to the square root of the film
 speed. You have a camera with f-stop numbers
 2.8, 4, 5.6, 11, 16, and 22. Which f-stop should
 you use to photograph fireworks if you are
 using a film speed of 64?
Simplifying Square Roots.
 Chapter 9.2 page 458
    Simplifying a Radical Expression
• A radical expression is in simplest form when:
a. No factor of the expression under the radical
  sign () has any perfect square factor.
b. There are no fractions under the radical sign,
  and no radical sign in the denominator of any
  fraction.
• Tell whether the expression 3√5 is in simplest
  form based on the above criteria.
• Yes, because you can’t take the square root of 5.
           Simplify:
• 180 =

• 63 =

• 98 =

• 250 =
• 24s2 =

• 54t2 =

• 300x =

• 63b2 =
• 75x2y =




• 7200m2n2 =
             Simplify:
• 15/16 =




• 32/n2 =
              Simplify:
• √11/36 =




• √35/144 =
          Accident Investigation
• After a car accident, a police officer measures
  the length l (in feet) of a car’s skid marks. The
  expression 27l gives the car’s speed in miles
  per hour at the time the brakes were applied.
• Write the expression 27l in simplest form.
• 3•3•3•l             Broken down into primes
• 33l                 Pulling out pairs
• The length of the skid marks are 125 feet long,
  so we can substitute that in for l and solve.
• 33l = 33(125)
• 33•5•5•5 = 3•515 ≈ 15•4 ≈ 60 miles

				
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