Transcript Square Roots - School helper

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
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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/k5/div_rules.ppt#1
• http://www.lessontutor.com/lw6.html
Inverse Operations
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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
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√0 = 0
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
CUBE
√49 = 7
∛0 = 0
√64 = 8
∛1 = 1
√81 = 9
∛8 = 2
√100 = 10 ∛27 = 3
√121 = 11 ∛64 = 4
√144 = 12 ∛125 = 5
√169 = 13
FOURTH
4√0
=0
4√1 = 1
4√16 = 2
4√81 = 3
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.
2.
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5.
6.
7.
8.
4
16
36
64
121
144
225
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
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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