Lesson Plan 0 - Quia
Algebra 1 Lesson Notes 2.7A Date _______________
Objective: Find square roots.
Square Root of a number: If b2 = a, then b is a square root of a.
Notation: [pic] indicates the square root of a.
radical symbol [pic]
radicand
All positive real numbers have two square roots, one positive square root (the principal square root) and one negative square root.
The square of 7 is 72 = 49. The square of –7 is (–7)2 = 49.
Note: This is a very important detail.
To square a negative number, you MUST use parentheses!
[pic] indicates the positive and negative square roots
[pic] indicates the positive square root
[pic] indicates the negative square root
Zero has one square root, 0.
Negative real numbers have no real square roots. Why?
Example 1 (p 110): Find square roots
a. [pic]
b. [pic]
c. [pic]
d. [pic]
Perfect Squares: The square of a number is called its perfect square.
Conversely, a number is a perfect square if its square roots are integers.
Helpful advice: Become familiar with perfect squares!!! List the squares of 1-20.
Example 2 (p 111): Approximate a square root
The cover of a square box has an area of 220 sq. in. Estimate the length
of a side of the cover to the nearest inch.
Notation: ≈ indicates approximately equal to
( HW A7 pp 113-116 #4-14 even, 15-23, 47-48
Algebra 1 Lesson Notes 2.7B Date _______________
Objective: Compare real numbers.
irrational number: a number that cannot be written as a quotient of two
integers.
The decimal form of an irrational number does not terminate and does not repeat.
Example 5: Rewrite a conditional statement in if-then form
Tell whether the statement is true or false. If false, give a counterexample.
a. No integers are irrational numbers.
b. All real numbers are rational numbers.
c. No square roots are rational numbers.
d. All integers are rational numbers.
( CW: p 114 #30-33 (Using the Venn diagram to make conclusions)
Example 3 (p 112): Classify numbers
Classify each of the following numbers.
Real Rational Irrational Integer Whole
Number number number number number number
[pic]
[pic]
[pic]
Example 4 (p 112) Graph and order real numbers
Order the numbers from least to greatest: [pic], [pic], – 3, [pic], [pic]
( HW A8 pp 113-116 #24-28 even, 34-42, 49-50, PQ 2.6-2.7 #1-6
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Irrational numbers
Real numbers
Rational numbers
Integers
Whole numbers
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