3 Vocabulary Objectives square root rational numbers perfect square irrational numbersreal numbers repeating decimalnatural numbers terminating decimalwhole numbers IntegersObjectivesEvaluate expressions containing square roots.Classify numbers within the real number system.
4 Square RootsA number that is multiplied by itself to form a product is called a square root of that product. The operations of squaring and finding a square root are inverse operations.The radical symbol , is used to represent square roots. Positive real numbers have two square roots.4 4 = 42 = 16= 4Positive squareroot of 16(–4)(–4) = (–4)2 = 16Negative square root of 16–= –4
5 Perfect SquaresThe nonnegative square root is represented by The negative square root is represented by –A perfect square is a number whose positive square root is a whole number. Some examples of perfect squares are shown in the table.14916253649648110002122232425262728292102
6 The expression does not represent a real number because there is no real number that can be multiplied by itself to form a product of –36.Reading Math
7 Finding Square Roots of Perfect Squares Find each square root.A.Think: What number squared equals 16?42 = 16Positive square root positive 4.= 4B.Think: What is the opposite of the square root of 9?32 = 9= –3Negative square root negative 3.
8 Finding Square Roots of Perfect Squares Find the square root.Think: What number squared equals ?2581Positive square root positive59
9 Find the square root. 1a. 22 = 4 = 2 1b. 52 = 25 Try This!Find the square root.1a.22 = 4Think: What number squared equals 4?= 2Positive square root positive 2.1b.Think: What is the opposite of the square root of 25?52 = 25Negative square root negative 5.
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