Download Ch. 1-2 Online Notes

Name
Class
Date
Lesson 1-2 Irrational Numbers and Square Roots
Lesson Objective
Common Core Standards
To find and estimate square roots and to
classify numbers as rational or irrational
The Number System: 8.NS.1, 8.NS.2
Expressions and Equations: 8.EE.2
Vocabulary
The square root of a number is a number that when multiplied by itself is equal to
the given number.
a
b
numbers that cannot be written in the form , where a is
Irrational numbers are any integer and b is any nonzero integer.
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A perfect square is a number that is the square of a whole number.
set of rational and irrational numbers.
The real numbers are the
Examples
a. 81
b. 9  9 5 81 and 29  29 5 81
The two square roots of 81 are 9 and 29 . 1
36
1
1
1
1

5
and 2 
6
6
6
36
The two square roots of
2 Estimating a Square Root Estimate the value
81
of 2 70 to the nearest integer and to the
nearest tenth.
1
26 5
1
are 1 and 1 ·
6
6
36
Since 70 is closer to 70.56 than to 68.89, 2 70 ¯ 28.4 .
64
70
8
9
Since 70 is closer to 64 than it is to 81, 2 70 ¯ 28 .
1
36
70
70.56
68.89
83
84
Quick Check
1. Find the square roots of each number.
a. 36
b. 1
6, 26
1, 21
c. 1
16
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
1 Finding Square Roots of Perfect Squares Find the two square roots of each number.
1, 1
24
4
2. Estimate the value of 38 to the nearest integer and to the nearest tenth. 6; 6.2
4
441198_C3_Ch1_WKbk_Ver-1.indd 4
Course 3 Lesson 1-2
Daily Notetaking Guide
10/10/12 4:19 PM
Name
Class
Date
Examples
3 Comparing Square Roots Which is greater, 28 or 5.1?
First, estimate the value of the square root to the nearest tenth. 28 ¯ 5.3
Since 5.3
. 5.1, 28 . 5.1.
4 Surface Area of a Sphere The formula S.A. 5 13r2 gives the approximate
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surface area S.A. in square units of a sphere with radius r. Find the radius of
a sphere with surface area 650 square units.
S.A. 5 13r2 ← Use the formula for the surface area of a sphere.
650 5 13r2 ← Substitute 650
650
5 r2
13
50 ¯ r2
50 ¯
for S.A.
← Divide each side by 13
to isolate r.
← Simplify.
r 2 ← Find the positive square root of each side. Use a calculator.
7.1 ¯ r ← Round to the nearest tenth.
The radius of a sphere with surface area 650 square units is about 7.1
units.
5 Classifying Real Numbers Is each number rational or irrational?
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Explain.
a. 29333.3
b. 4
c.
7
9
Rational
; the decimal repeats.
Rational
; the number can be written as the ratio
Irrational ; 90 is not a
90 Irrational
d. 6.363663666 . . .
perfect
43
.
9
square.
; the decimal does not terminate or repeat.
Quick Check
3. Which is greater
20 or 4.7?
4.7
4. Use the formula S.A. 5 13r2 to find the radius of a sphere with a surface
area of 520 square units. Round to the nearest tenth of a unit.
6.3 units
_
5. Is 0.6 rational or irrational? Explain.
Rational; the decimal repeats.
Daily Notetaking Guide
441198_C3_Ch1_WKbk_Ver-1.indd 5
Course 3 Lesson 1-2
5
10/10/12 4:19 PM