Square Roots Chapter 9.1 page 453

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Square RootsChapter 9.1 page 453

• What does it mean?
• Before--you found squares of numbers.
• Now--youll find and approximate square roots of
  numbers.
• Why!!!!!! So you can solve equations.

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Square Root Websites

• http//www.purplemath.com/modules/radicals.htm
• http//www.aplusmath.com/games/matho/MultMatho.htm
  l
• 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.ppt2
• http//www.nebo.edu/misc/learning_resources/ppt/k-
  5/div_rules.ppt1
• http//www.lessontutor.com/lw6.html

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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.

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Below is a list of the most common roots.

• SQUARE CUBE FOURTH
• v0 0 v49 7 ?0 0
  4v0 0
• v1 1 v64 8 ?1 1
  4v1 1
• v4 2 v81 9 ?8 2 4v16
  2
• v9 3 v100 10 ?27 3 4v81
  3
• v16 4 v121 11 ?64 4
• v25 5 v144 12 ?125 5
• v36 6 v169 13

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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.

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Find the square roots of the number.

1. 4
2. 16
3. 36
4. 64
5. 121
6. 144
7. 225
8. 256

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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

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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

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Approximate to the nearest integer.

• 1. ?10
• 2. -?84
• 3. ?151
• 4. -?200

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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.

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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

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Solve the equations.

1. a2 9
2. n2 25
3. 361 x2
4. 400 y2

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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.

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Evaluate when a 12 and b 4.

• ?a b
• ?b2 a
• 3?ab 1
• Evaluate when a 48 and b 12
• ?a - b

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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

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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?

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Simplifying Square Roots.Chapter 9.2 page 458
18
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 3v5 is in simplest
  form based on the above criteria.
• Yes, because you cant take the square root of 5.

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Simplify

• ?180
• ?63
• ?98
• ?250

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• ?24s2
• ?54t2
• ?300x
• ?63b2

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• ?75x2y
• ?7200m2n2

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Simplify

• ?15/16
• ?32/n2

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Simplify

• v11/36
• v35/144

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Accident Investigation

• After a car accident, a police officer measures
  the length l (in feet) of a cars skid marks.
  The expression ?27l gives the cars speed in
  miles per hour at the time the brakes were
  applied.
• Write the expression ?27l in simplest form.
• ?333l 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?3555 35?15 154 60 miles