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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−2

−3

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Irrational numbers

Real numbers

Rational numbers

Integers

Whole numbers

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