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Transcript
Notes for Lesson 1-3: Real Numbers and the Number Line
Vocabulary:
Square root - A number that is multiplied by itself to form a product
Radicand – The expression under the radical sign
Radical – An expression made up of a radical symbol and a radicand
Perfect square - A number whose positive square root is a whole number
1 - Finding the square roots of perfect squares
Example: Find the square root
√81 = 9 𝑏𝑒𝑐𝑎𝑢𝑠𝑒 92 = 81
9
√
16
=
3
4
√169 = 13
3
9
4
16
𝑏𝑒𝑐𝑎𝑢𝑠𝑒 ( )2 =
√2.25 = 1.5
Square roots of many numbers are not whole numbers, like the square root of 15. However, we can use the
square roots of perfect squares to estimate the square roots of other numbers.
15
32  9 and 42  16
15 is closer to 16
Do √34 and √386
3.9  15.21 and 3.8  14.44
2
2
So the 15 is closer to 3.9
2 - Application
Nancy wants to plant a garden in a square shaped plot. She has enough vegetables to cover 19 sq. ft. Estimate
to the nearest tenth the length of the side of the square plot she can plant.
3 - Classifying Real Numbers
Vocabulary:
Set – A well-defined collection of objects
Element of a Set – A member of a set
Subset – A set consisting of elements from the given set
Natural numbers - The counting numbers
Whole Numbers - The natural numbers and zero (numbers that represent the amount of something)
Integers - Whole numbers and their opposites
a
Rational numbers - Numbers that can be expressed as a fraction
b
a
Irrational numbers - Numbers that cannot be expressed as a fraction
b
Real numbers - The set of all rational and irrational numbers
Examples: Classifying real numbers
8
belongs to which sets of real numbers
9
answer: rational
18 belongs to which sets of real numbers
answer: natural, whole, integer, rational
20 belongs to which sets of real numbers
answer: irrational
4
belongs to which sets of real numbers
9
6 belongs to which sets of real numbers
7
answer: rational
answer: integers, rationals
4 – Comparing real numbers and graphing them on a number line.
Vocabulary:
Inequality – A mathematical sentence that compares the values of two expressions
Using > < ≥ ≤ to compare the values of two numbers.
1
Compare √18 𝑎𝑛𝑑 4 3
Compare √129 𝑎𝑛𝑑 11.2
5 – Graphing and Ordering Real Numbers
2
What is the order of √4, 0.4, − 3 , √2, 𝑎𝑛𝑑 − 1.5 from least to greatest
-1.5
-2/3
√2
0.4
7
What is the order of 3.5, −2.1, √9, − 2 , 𝑎𝑛𝑑 √5 from least to greatest.
-7/2
-2.1
√5
3.5