2-8 Square Roots and Real Numbers Objective: To find square roots, to classify numbers, and to graph solutions on the number line.

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Presentation transcript:

2-8 Square Roots and Real Numbers Objective: To find square roots, to classify numbers, and to graph solutions on the number line.

Drill #26 Rewrite each fraction in simplest form:

Perfect Squares Perfect Squares: The perfect squares are numbers that have whole number square roots. The first 7 are represented by the squares above

Squares Table xx

Square Root ** (21.) Definition: Ifthen x is a square root of y. NOTE: Once the square root is evaluated, the radical is removed. Examples:

Classwork Find the following square roots:

Irrational Number Definition: Numbers that cannot be expressed in the form a/b, where a and b are integers and b = 0. Irrational numbers are decimals that do not terminate and do not repeat. Square roots of numbers that are not perfect squares are irrational. Examples:

Classwork #26* Name the set or sets of numbers to which each of the following real numbers belongs:

Completeness Property for Points on the Number Line Definition: Each real number corresponds to exactly one point on the number line. Each point on the number line corresponds to exactly one real number.

Classwork #26* Graphing Solution Sets Use the replacement {-2, -1, 0, 1, 2 } to find a solution set for the following x > 0 What if we didn’t have a replacement? What would the solution set look like?

Graphing Inequalities Example x > 5 When graphing inequalities 1.If graphing > or < or = put an open circle on the number to indicate that the graph does not include this number. 2.If graphing > or < put an closed circle on the number to indicate that the graph does not include this number. 3.If graphing > or > draw a line pointing to the right to include all larger numbers greater in the solution 4.If graphing < or < draw a line pointing to the left to include all smaller numbers in the solution 5.If graphing =

Graphing inequalities The line (graph) should be pointing in the same direction as the inequality. > > graphs point to the right  < < graphs point to the left  get open circles get closed circles = gets open circles and arrows going right and left

Examples x = -2 x > -2 x <