Presentation on theme: "9.1 To evaluate square roots Objective Part I Evaluating Square Roots"— Presentation transcript:
1 9.1 To evaluate square roots Objective Part I Evaluating Square Roots Square Root of a NumberIf , then b is a square root of a.Example: If 32 = 9, then 3 is a square root of 9.All positive real numbers have two square roots:a positive square root (or principal square root) anda negative square root.Square roots are written with a radical symbolThe number or expression inside a radical symbol is the radicand.
2 The positive and negative square roots MeaningPositive square rootNegative square rootThe positive and negative square rootsSymbolExampleYou may use the table on pg 811 to help find square roots
3 You may not have a negative radicand Example 1Evaluate the expression.a.Positive square rootb.Negative square rootc.Square root of zerod.Two square rootse.No real square rootYou may not have a negative radicand
4 2.236068… non ending not repeating Perfect squares: occur when a number is multiplied by itself.EX: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225Rational numbers: can be written as a fractionEX:4= 3An irrational number is a number that cannot be written as a fraction.They include all non ending non repeating decimalsEX: … non ending not repeatingThe square roots of numbers that are not perfect squares are irrational numbers and must be written using the radical symbol or approximated.
5 Example 2 Irrational Evaluate the expression. a. b. c. d. 7 is NOT a perfect square
6 Evaluate the expression when a = 1, b = –2, and c = –3 . Example 3Evaluate the expression when a = 1, b = –2, and c = –3 .Substitute values
7 Example 4Evaluate the expression.Expression represents two numbers