advertisement

Chapter 4 Lesson 4.5 By definition 25 is the number you would multiply times itself to get 25 for an answer. Because we are familiar with multiplication, we know that 25 = 5 Numbers like 25, which have whole numbers for their square roots, are called perfect squares You need to memorize at least the first 15 perfect squares Square root Perfect square 1 1 = 1 81 4 4 = 2 100 100 = 10 9 9 = 3 121 121 = 11 16 16 = 4 144 144 = 12 25 25 = 5 169 169 = 13 36 36 = 6 196 196 = 14 49 49 = 7 225 225 = 15 64 64 = 8 Perfect square Square root 81 = 9 Every whole number has a square root Most numbers are not perfect squares, and so their square roots are not whole numbers. Most numbers that are not perfect squares have square roots that are irrational numbers Irrational numbers can be represented by decimals that do not terminate and do not repeat The decimal approximations of whole numbers can be determined using a calculator Obj: To find the square root of a number • Find the square roots of the given numbers • If the number is not a perfect square, use a calculator to find the answer correct to the nearest thousandth. 81 81 = 9 37 37 6.083 158 158 12.570 Obj: To find the square root of a number • Find two consecutive whole numbers that the given square root is between • Try to do this without using the table 18 16 = 4 and 25 = 5 so 18 is between 4 and 5 115 100 = 10 and 121 = 11 so 115 is between 10 and 11 Multiplying radicals The product of the square roots of two numbers is the same as the square root of the product of the numbers Examples: 3 12 = 36 7 11 = 77 =6 Simplify the following expressions -4 = -(2) 764 + 9 = 7 8 + 9 = 56 + 9 = 65 525 + 49 = 5 5 + 7 = 25 + 7 = 32 Simplify the following expressions 4 81 4 = 81 1 – 36 = 1 144 2 9 1 6 1 – 12 2 = 12 1 – 12 = 1 = 12 Rationalizing the Denominator When the radical in the denominator is not a perfect square A form of 1 A form of 1 A form of 1 Simplify integers Simplify integers Simplified radical form No factor inside the radical should be a perfect square. 18 = 9 2 = 9 2 = 3 2 108 = 36 3 = 36 3 = 6 3 96 = 16 6 = 16 6 = 4 6 Graphing real numbers The graph of a number is a dot placed where the number would be on the number line Graph the number: -10 -5 1 32 0 5 10 5 10 Graph the number: -8.5 -10 -5 0 Graphing inequalities The symbol, [ , means that the point is included in the graph The symbol, ( , means that the point is not included in the graph Graph the real numbers between -4 and 6 ( -10 -5 ) 0 5 10 Graph the real numbers less than 8 ) -10 -5 0 5 10 Graphing inequalities The symbol, [ , means that the point is included in the graph The symbol, ( , means that the point is not included in the graph Graph the inequality: x > -3 ( -10 -5 0 5 10 5 10 Graph the inequality: x 4 ] -10 -5 0