Square Roots and Irrational Numbers PDF

O.B. Montessori Center Junior High School MATH 7 Grade and Section Campus TEACHER LET’S INVESTIGATE: Which of these can form a larger square (w/ no excess)? 4 6 9 LET’S INVESTIGATE: Draw the larger square that you formed. LET’S INVESTIGATE: Which of these can form a larger square (w/ no exces...

O.B. Montessori Center Junior High School MATH 7 Grade and Section Campus TEACHER LET’S INVESTIGATE: Which of these can form a larger square (w/ no excess)? 4 6 9 LET’S INVESTIGATE: Draw the larger square that you formed. LET’S INVESTIGATE: Which of these can form a larger square (w/ no excess)? 2 3 2 3 4 Squares 9 Squares Perfect Square Numbers  Perfect Square Numbers Perfect Squares Numbers are numbers that are obtained by squaring an integer.  Warm-up! Complete the table: Exponential Perfect Exponential Perfect Exponential Perfect Form Square Form Square Form Square 12 92 172 22 102 182 32 112 192 42 122 202 52 132 212 62 142 222 72 152 232 82 162 242 252  Exponential Perfect Form Square 12 1 Warm-up! 22 4 32 9 42 16 52 25 62 36 72 49 82 64  Exponential Perfect Form Square 92 81 102 100 Warm-up! 112 121 122 144 132 169 142 196 152 225 162 256  Exponential Perfect Form Square Warm-up! 172 289 182 324 192 361 202 400 212 441 222 484 232 529  Warm-up! Exponential Perfect Form Square 242 576 252 625 Perfect Square Numbers SQUARE ROOTS  BJECTIVES: List down the first 25 perfect squares Illustrate square root using geometric models Plot irrational numbers on the number line (approximation) Perfect Exponential Radical Square Form Form 100 102=10x10 100 = 10 36 62=6x6 36 = 6 81 92=9x9 81 = 9 144 122=12x12 144 = 12 225 152=15x15 225 = 15 What is square root? 2 1 4 1 1 1= 1 2 4= 2 What is square root? 3 4 9 16 3 4 9= 3 16 = 4 What is square root? 𝑏=𝑎 The symbol is the radical sign; the number 𝑏 inside the radical is the radicand, and 𝑎 is the root, specifically, the square root.(p. 51) NOTE: The square root of a negative number DOES NOT EXIST (NOT REAL).  Take note! 2 2 10 = 100 (−10) = 100 102 𝑎𝑛𝑑 (−10)2 𝑎𝑟𝑒 𝑏𝑜𝑡ℎ 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 100. Hence, 100 has two possible square roots, 10 and − 10. 10 is the principal root. STOP SLOW GO ACTIVITY Find the principal root of each given. a.) 25 d.) 81 b.) 16 e.) 144 c.) 49 f.) 169 ACTIVITY Find the principal root of each given. 𝑔) 225 = ℎ) 100= i) 400 = O.B. Montessori Center Junior High School MATH 7 Grade and Section Campus TEACHER  BJECTIVES: List down the first 25 perfect squares Illustrate square root using geometric models Plot irrational numbers on the number line (approximation)  81 = 9 1= 1 100 = 10 25 = 5 169 = 13 64 = 8 400 = 20 4= 2 225 = 15 49 = 7  9= 3 16 = 4 121 = 11 36 = 6 196 = 14 144 = 12 625 = 25 256 = 16 289 = 17 441 = 21 324 = 18 484 = 22 576 = 24 361 = 19 529 = 23 Drill #7: Square roots IRRATIONAL NUMBERS IRRATIONAL NUMBERS 1 2 3 4 5 6 7 8 9 10 IRRATIONAL NUMBERS The decimal value of any irrational number is nonterminating and nonrepeating. (p. 52) 2 3 5 6 7 8 10 EXAMPLES OF IRRATIONAL IRRATIONAL NUMBERS Though we cannot manually enumerate all the digits of an irrational number, we can estimate or approximate its value. ✔ Look for the nearest perfect square before and after the given irrational number. EXERCISE Between which two consecutive integers does each irrational number lie? STEP 1: Identify the perfect square closest to the number. 9 < 10 < 16 STEP 2: Find the square root of the three numbers. 3 < 10 < 4 EXERCISE Between which two consecutive integers does each irrational number lie? STEP 1: Identify the perfect square closest to the number. 16< 18 < 25 STEP 2: Find the square root of the three numbers. 4 < 18 < 5 EXERCISE Between which two consecutive integers does each irrational number lie? a.) 12 b.) 20 EXERCISE Between which two consecutive integers does each irrational number lie? c.) 14 d.) 40 EXERCISE Between which two consecutive integers does each irrational number lie? e.) 68 EXERCISE Label the number line and plot each set of numbers. a.) 12 -5 -4 -3 -2 -1 0 1 2 3 4 5 EXERCISE Label the number line and plot each set of numbers. b.) 20 -5 -4 -3 -2 -1 0 1 2 3 4 5 EXERCISE Label the number line and plot each set of numbers. c.) 14 -5 -4 -3 -2 -1 0 1 2 3 4 5 EXERCISE Label the number line and plot each set of numbers. d.) 40 -5 -4 -3 -2 -1 0 1 2 3 4 5 EXERCISE Label the number line and plot each set of numbers. e.) 68 O.B. Montessori Center Junior High School MATH 7 Grade and Section Campus TEACHER Each irrational number lies between two consecutive integers. Determine these consecutive integers for each item below. 7= 40 = 10 = 29 = 85 = 220 =  BJECTIVES: Illustrate the Real Number System using a Venn Diagram Give examples of each subset of the set of Real numbers (Counting, Whole, Integer, Rational and Irrational)  GROUP THE NUMBERS 1 -1 2 0.5 2 1 3 5 𝜋 -4 4 0.25 2 4 0 3 3 -2 -3  GROUP THE NUMBERS 1 -1 2 0.5 2 1 3 5 𝜋 -4 4 0.25 2 4 0 3 3 -2 -3 NATURAL NUMBERS  SET OF REAL NUMBERS NATURAL RATIONALNUMBERS ℕ INTEGERS ⮚ used for counting. ⮚ {1, 2, 3, 4, 5, …} WHOLE ⮚ always positive NATURAL Examples: 1, 2, 5, 8, 17  GROUP THE NUMBERS -1 0.5 2 1 3 5 𝜋 -4 0.25 2 4 0 3 -2 -3 NATURAL WHOLE NUMBERS NUMBERS 1 2 3 4 NATURAL RATIONALNUMBERS 𝕎 INTEGERS ⮚ Counting numbers, including zero. WHOLE ⮚ {0, 1, 2, 3, 4, 5, …} NATURAL Examples: 0, 2, 3, 5, 8, 17  GROUP THE NUMBERS -1 0.5 2 1 3 5 𝜋 -4 0.25 2 4 3 -2 -3 INTEGERS WHOLE NUMBERS 1 2 0 3 4 NATURAL RATIONALNUMBERSℤ 𝑍𝑎ℎ𝑙𝑒𝑛 ⮚ Whole numbers, including the negative INTEGERS counting numbers. ⮚ {…, -2, -1, 0, 1, 2, …} WHOLE Examples: NATURAL -19, -8, -5, 0, 2, 3, 5, 8, 17  GROUP THE NUMBERS 0.5 2 1 3 5 𝜋 0.25 2 4 3 INTEGERS RATIONAL NUMBERS 1 2 -1 -2 0 3 4 -3 -4 NATURAL ℚ RATIONALNUMBERS𝑄𝑢𝑜𝑡𝑖𝑒𝑛𝑡 INTEGERS WHOLE NATURAL  GROUP THE NUMBERS 2 5 𝜋 3 RATIONAL NUMBERS IRRATIONAL NUMBERS 1 2 -1 -2 0.5 3 0 1 4 3 4 -3 -4 2 0.25 MATH JOKE Why did all the other numbers avoid talking with pi at the party? NATURAL NUMBERS IRRATIONAL SET OF REAL NUMBERS These are the sets that make up the Real Numbers: ℝ ℚ RATIONAL IRRATIONAL ℤ INTEGERS 𝕎 WHOLE ℕNATURAL  Do Basic: Page 56 Determine if each expression is rational, irrational or not real. a) 1 e) 15 b) 8 f) 1000 c) − 25 g) 400 d) − 121 h) −81 Example #1 Encircle the number/s which belong to the set. a.) Natural Number 123 -45 0 6.78 b.) Whole Number 123 -45 0 6.78 c.) Integer 123 -45 0 6.78 d.) Rational Number 123 -45 0 6.78 Example #1 Encircle the number/s which belong to the set. 𝟐 a.) Natural Number 27 49 1.00 𝟐 𝟑 b.) Whole Number 10 -4.4 -100 𝟔 c.) Integer -7 11 -0.4 17.00 𝟗𝟗 𝟕 d.) Rational Number -1 𝟏𝟐 𝟗 𝟏𝟏 Example #2 Check the set(s) to which each number belongs. 𝕊ummary Name 5 subsets of the Real numbers and give 1 example each. Rational or Irrational https://www.baamboozle.com/game/1122657