Download Chap 3 - 05

Lesson 3-1 Square Roots
Find each square root:
1. 81
Perfect squares – Numbers that can be
pictured in squares of dots.
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2.  144
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Square Root – the number of dots in
each row or column in the square.
49
If x2 = y, then x is a square root of y.
4.  225
5.  0.16
Principal square root – the positive
square root of a number.
Radical sign – the symbol
.
25 = 5
- 25 = -5
Solve:
6. x 2 
49
64
To find the square root of large
numbers, do upside down division.
225 = 3  3  5  5, so sq. root = 15.
7.
4
 y2
25
8. a 2  196
To find the square root of fractions,
just find the square root of each part.
Your answer will be a fraction.
Reduce.
9
= 3
4
16
9. 0.09  m 2
Glencoe Math App & Conn (2006) – Course 3
Lesson 3-2 Estimating Square Roots
Estimate to the nearest whole number:
1. 54
2.
35
Estimate square roots – Figure out
which two perfect squares the number
is between. Name the square root that
is closest.
79 is between
64 and
81 .
Subtract to find the closest one.
3. 170
4. 14.8
79 – 64 = 15 and 81 – 79 = 2, so 9 is
the closest square root.
For fractions and decimals, do the
same thing.
5. If you were to invest $100 in a bank
account for two years, your money
would earn interest daily and be worth
more when you withdrew it. If you had
$120 after two years, the interest rate,
written as a decimal, would be found
120  10
using the expression
.
10
Estimate this value.
Glencoe Math App & Conn (2006) – Course 3
Lesson 3-3 The Real Number System
Name all sets of numbers to which each
real number belongs:
1. 25
Real Numbers – include rational and
irrational numbers.
Rational
Numbers
Irrational
Integers
2.  12
Whole
3. 0.090909…
4. Estimate 8 and  2 to the nearest
tenth. Then graph on a number line.
Irrational Numbers – a number that cannot
be expressed as a fraction.
0.6666…. is rational because we can change
it into a fraction.
-2
-1
0
1
2
3
4
Compare to make a true sentence:
7
29
5. 3
8
3 is whole, integer, rational, real.
-4 is integer, rational, real.
3
is rational, real.
2
29 is irrational.
6. 3.2
10.4
7. The time in seconds that it takes an
object to fall d feet is 0.25 d . How
many seconds would it take for a
baseball that is hit 250 feet straight up in
the air to fall from its highest point to the
ground?
Glencoe Math App & Conn (2006) – Course 3
Lesson 3-4 The Pythagorean Theorem
Hypotenuse – opposite of the right
angle.
1. Find the length
of the kite string.
c ft.
12 ft.
Legs – The sides that form the right
angle.
hypotenuse
leg
5 ft.
2. The hypotenuse of a right triangle is
33 centimeters long and one of its legs is
28 centimeters. Find the length of the
other leg.
leg
Pythagorean Theorem:
a2 + b2 = c2
5 ft.
3. A 10-foot ramp is extended from the
back of a truck to the ground to help
movers load furniture onto the truck. If
the ramp touches the ground at a point 9
feet behind the truck, how high off the
ground is the top of the ramp?
a. about 1 foot
c. about 13.5 feet
b. about 4.4 feet
c. about 19 feet
4. The measures of three sides of a
triangle are 24 inches, 7 inches, and 25
inches. Determine whether the triangle
is a right triangle.
12 ft.
52 + 122 = c2
25 + 144 = c2
169 = c2
169 = 13 ft.
To determine if 3 sides form a right triangle
use Pythagorean Theorem:
1) Use the 2 smaller numbers for a and b .
2) Use the largest number for c.
15 in., 8 in., 17 in.
152 + 82 = 172
225 + 64 = 289
289 = 289 
Glencoe Math App & Conn (2006) – Course 3
Lesson 3-5 Using the Pythagorean Theorem
Same as yesterday:
1. A ramp to the entrance of a newly
constructed building must be built
according to accessibility guidelines
stated in the Americans with Disabilities
Act. If the ramp is 24.1 feet long and the
top of the ramp is 2 feet off the ground,
how far is the end of the ramp from the
entrance?
Pythagorean Theorem:
a2 + b2 = c2
2. Multiply the triple 5-12-13 by the
numbers 2, 3, 4 to find more
Pythagorean triples.
3. To save energy in a cold climate,
a house has a roof that slants from
the middle of the house to the
ground on the north side. The
house is 48 feet wide and 18 feet
tall. How long is the roof?
r ft
18 ft.
48 ft.
Glencoe Math App & Conn (2006) – Course 3
Lesson 3-6 Geometry: Distance on the Coordinate Plane
1. Graph the ordered pairs (0, -6) and
(5, -1). Then find the distance between
the two points.
2. Graph the ordered pairs (-1, 2) and
(7, -4) on a coordinate plane. Then find
the distance between the points.
Use Pythagorean Theorem to find the
distance between two points on the x-y
coordinate system.
Steps:
1. Graph the two points.
2. Draw a horizontal and vertical line
until the two meet.
3. Count the squares to find the length of
the two legs.
4. Use Pythagorean Theorem to find the
length between the two points.
Pythagorean Theorem:
a2 + b2 = c2
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4
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3
To find the distance between (0, -1) and
(3, 3).
1. Graph the two points.
2. Draw a horizontal & vertical line.
3. Count the spaces; 4 and 3.
4. 42 + 32 = c2
25 = c2
16 + 9 = c2
25 = c
5=c
Glencoe Math App & Conn (2006) – Course 3