Presentation on theme: "Square Roots and Real Numbers"— Presentation transcript:
1 Square Roots and Real Numbers 1-5Square Roots and Real NumbersHolt Algebra 1Warm UpLesson PresentationLesson Quiz
2 Warm Up Simplify each expression. 1. 62 2. 112 121 36 25 36 3. (–9)(–9)814.Write each fraction as a decimal.255220.127.116.11.5538–1567.5.3758.–1.83
3 Objectives Evaluate expressions containing square roots. Classify numbers within the real number system.
4 A 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 squareroot are inverse operations.The radical symbol , is used to represent square roots. Positive real numbers have twosquare roots.= 4Positive squareroot of 164 4 = 42 = 16(–4)(–4) = (–4)2 = 16–= –4Negative squareroot of 16
5 The nonnegative square root is represented by The 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 Example 1: Finding Square Roots of Perfect SquaresFind each square root.A.Think: What number squared equals 16?42 = 16Positive square root positive 4.= 4B.Think: What is the opposite of thesquare root of 9?32 = 9= –3Negative square root negative 3.
8 Example 1C: Finding Square Roots of Perfect SquaresFind the square root.Think: What number squared equals ?2581Positive square root positive .59
9 The square roots of many numbers like , are not whole numbers The square roots of many numbers like , are not whole numbers. A calculator can approximate the value of as Without a calculator, you can use square roots of perfect squares to help estimate the square roots of other numbers.
10 Check It Out! Example 2What if…? Nancy decides to buy more wildflower seeds and now has enough to cover 38 ft2. What is the side length of a square garden with an area of 38 ft2?Use a guess and check method to estimateGuess = too lowis greater than 6.1.Guess = too highis less than 6.2.A square garden with a side length of 6.2 ft would have an area of ft ft is close to 38, so 6.2 is a reasonable answer.
11 All numbers that can be represented on a number line are called real numbers and can be classified according to their characteristics.
12 Natural numbers are the counting numbers: 1, 2, 3, … Whole numbers are the natural numbers and zero:0, 1, 2, 3, …Integers are whole numbers and their opposites: –3, –2, –1, 0, 1, 2, 3, …Rational numbers can be expressed in the form ,where a and b are both integers and b ≠ 0: , , .ab127910
13 Terminating decimals are rational numbers in decimal form that have a finite number of digits:1.5, 2.75, 4.0Repeating decimals are rational numbers indecimal form that have a block of one or moredigits that repeat continuously: 1.3, 0.6, 2.14Irrational numbers cannot be expressed in the form . They include square roots of whole numbers that are not perfect squares and nonterminating decimals that do not repeat: ,, ab
14 Example 3: Classifying Real Numbers Write all classifications that apply to eachReal number.A. –3232 can be written as a fraction and a decimal.321–32 = – = –32.0rational number, integer, terminating decimalB. 55 can be written as a fraction and a decimal.515 = = 5.0rational number, integer, whole number, naturalnumber, terminating decimal
15 Write all classifications that apply to each real number. Check It Out! Example 3Write all classifications that apply to each real number.7 can be written as a repeating decimal.493a. 74967 9 = 7.444… = 7.4rational number, repeating decimal3b. –1232 can be written as a fraction and a decimal.–12 = – = –12.012 1rational number, terminating decimal, integer3c.The digits continue with no pattern.= …irrational number
16 Lesson QuizFind each square root.3712-18.104.22.168.–5. The area of a square piece of cloth is 68 in2.How long is each side of the piece of cloth?Round your answer to the nearest tenth of aninch.8.2 in.Write all classifications that apply to each real number.rational, integer, whole number, natural number, terminating decimal6. 17. –3.89rational, repeating decimal8.irrational
17 Sec 1-5 Vocab into Definitions section of notebook P. 35-36, #’s 11-40 AssignmentSec 1-5 Vocab into Definitions section of notebook P , #’s 11-40