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ESTIMATING SQUARE ROOTS. 55 is between 7 and 8 because 55 is between 49 and 64. Additional Example 1A: Estimating Square Roots of Numbers. Each square root is between two integers. Name the integers. Explain your answer. Think: What are perfect squares close to 55?. 55. 49 < 55. 7 2 = 49.
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55 is between 7 and 8 because 55 is between 49 and 64. Additional Example 1A: Estimating Square Roots of Numbers Each square root is between two integers. Name the integers. Explain your answer. Think: What are perfect squares close to 55? 55 49 < 55 72 = 49 64 > 55 82 = 64
Classifying Real Numbers Types: RATIONAL: 2 types: repeating decimals or terminating ( number stops) IRRATIONAL: is ALWAYS a nonrepeating & nonterminating decimal. ( Includes all of the square roots that are NOT perfect squares)
Classifying Square Roots 1. PERFECT SQUARES ( listed on the chart) **RATIONAL** & Terminating (ALL whole numbers) 2. Non-Perfect Square Roots are **IRRATIONAL** So they are Non-repeating DECIMALS
HOMEWORKSKILLS PRACTICEpg. 455 #2-4pg. 458 #17-20pg. 459 #1-9No Volcabulary
Logical ReasoningFill in the blank with the words always, sometimes, or never. 1. A real number is ________ a rational number. SOMETIMES Both 5 and are real numbers, but 5 is rational and is irrational.
Logical ReasoningFill in the blank with the words always, sometimes, or never. 2. An irrational number is _________ a real number. ALWAYS All numbers are real numbers.
Logical ReasoningFill in the blank with the words always, sometimes, or never. 3. A negative integer is _____________ an irrational number. NEVER Integers are always rational numbers because they are terminating.
Logical ReasoningFill in the blank with the words always, sometimes, or never. 4. The square root of a number is ________ an irrational number. SOMETIMES is rational because it is a perfect square, but the is not a perfect square—and therefore is irrational.
16 2 4 2 = = 2 Additional Example 1: Classifying Real Numbers Write all names that apply to each number. A. 5 is a whole number that is not a perfect square. 5 irrational, real B. –12.75 –12.75 is a terminating decimal. rational, real 16 2 C. whole, integer, rational, real
9 = 3 81 3 9 3 = = 3 Check It Out: Example 1 Write all names that apply to each number. 9 A. whole, integer, rational, real –35.9 –35.9 is a terminating decimal. B. rational, real 81 3 C. whole, integer, rational, real
0 3 = 0 Additional Example 2: Determining the Classification of All Numbers State if each number is rational, irrational, or not a real number. A. 21 irrational 0 3 B. rational
2 3 2 3 4 9 = Additional Example 2: Determining the Classification of All Numbers State if each number is rational, irrational, or not a real number. C. –4 not a real number 4 9 D. rational
Check It Out: Example 2 State if each number is rational, irrational, or not a real number. A. 23 is a whole number that is not a perfect square. 23 irrational 9 0 B. not a number, so not a real number
8 9 8 9 64 81 = Check It Out: Example 2 State if each number is rational, irrational, or not a real number. C. –7 not a real number 64 81 D. rational
4 • 9 3 4 3 8 Find a real number between –2 and –2 . 5 8 Possible answer –2 . Lesson DAILY GRADE Write all names that apply to each number. 16 2 2. – 1. 2 real, irrational real, integer, rational State if each number is rational, irrational, or not a real number. 25 0 4. 3. rational not a real number 5.
