page 142 & spiral review answers
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Page 142 & Spiral Review Answers. Student Learning Goal Chart. Lesson Reflections 3-8. Pre-Algebra Learning Goal Students will understand rational and real numbers. Students will understand rational and real numbers by being able to do the following:. - PowerPoint PPT PresentationTRANSCRIPT
Page 142 & Spiral Review Answers
Pre-Algebra
3-8 Squares and Square Roots
Student Learning Goal Chart
Lesson Reflections
3-8
Pre-Algebra Learning Goal
Students will understand rational and real numbers.
Students will understand rational and real numbers by being able to do the following:
• Learn to write rational numbers in equivalent forms (3.1)
• Learn to add and subtract decimals and rational numbers with like denominators (3.2)
• Learn to add and subtract fractions with unlike denominators (3.5)
• Learn to multiply fractions, decimals, and mixed numbers (3.3)
• Learn to divide fractions and decimals (3.4)
• Learn to solve equations with rational numbers (3.6)
• Learn to solve inequalities with rational numbers (3-7)
• Learn to find square roots (3-8)
Pre-Algebra
3-8 Squares and Square Roots
Today’s Learning Goal Assignment
Learn to find square roots.
Squares and Square Roots
Pre-Algebra
3-8 Squares and Square Roots
Pre-Algebra HW
Page 148
#1-13 all
Pre-Algebra
3-8 Squares and Square Roots3-8 Squares and Square Roots
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
3-8 Squares and Square Roots
Warm UpSimplify.
Pre-Algebra
3-8 Squares and Square Roots
25 64
144 225
400
1. 52 2. 82
3. 122 4. 152
5. 202
Pre-Algebra
3-8 Squares and Square Roots
Problem of the DayA Shakespearean sonnet is a poem made up of 3 quatrains (4 lines each), and a couplet (2 lines). Each line is in iambic pentameter (which means it has 5 iambic feet). So, how many iambic feet long is a Shakespearean sonnet?
70
Pre-Algebra
3-8 Squares and Square Roots
Today’s Learning Goal Assignment
Learn to find square roots.
Squares and Square Roots
Pre-Algebra
3-8 Squares and Square Roots
Vocabularyprincipal square rootperfect square
Pre-Algebra
3-8 Squares and Square Roots
Think about the relationship between the area of a square and the length of one of its sides.
Taking the square root of a number is the inverse of squaring the number.
Every positive number has two square roots, one positive and one negative. One square root of 16 is 4, since 4 • 4 = 16. The other square root of 16 is –4, since (–4) • (–4) is also 16. You can write the square root of 16 as ±4, meaning “plus or minus” 4.
area = 36 square unitsside length = 36 = 6 units
62 = 36 36 = 6
Pre-Algebra
3-8 Squares and Square Roots
The numbers 16, 36, and 49 are examples of perfect squares. A perfect square is a number that has integers as its square roots. Other perfect squares include 1, 4, 9, 25, 64, and 81.
When you press the key on a calculator, only the nonnegative square root appears. This is called the principal square root of the number.
+ 16 = 4 – 16 = –4
–49 is not the same as – 49. A negative number has no real square root.
Helpful Hint
Pre-Algebra
3-8 Squares and Square Roots
Additional Example: 1 Finding the Positive and Negative Square Roots of a Number
Find the two square roots of each number.
7 is a square root, since 7 • 7 = 49.
–7 is also a square root, since –7 • –7 = 49.
10 is a square root, since 10 • 10 = 100.
–10 is also a square root, since –10 • –10 = 100.
49 = –7–
49 = 7
100 = 10
100 = –10–
A. 49
B. 100
C. 225
15 is a square root, since 15 • 15 = 225.225 = 15
225 = –15– –15 is also a square root, since –15 • –15 = 225.
Pre-Algebra
3-8 Squares and Square Roots
A. 25
Try This: Example 1
5 is a square root, since 5 • 5 = 25.–5 is also a square root, since –5 • –5 = 25.
12 is a square root, since 12 • 12 = 144.
–12 is also a square root, since –12 • –12 = 144.
25 = –5–25 = 5
144 = 12
144 = –12–
Find the two square roots of each number.
B. 144
C. 289289 = 17
289 = –17–
17 is a square root, since 17 • 17 = 289.
–17 is also a square root, since –17 • –17 = 289.
Pre-Algebra
3-8 Squares and Square Roots
132 = 169
The window is 13 inches wide.
Find the square root of 169 to find the width of the window. Use the positive square root; a negative length has no meaning.
Additional Example 2: ApplicationA square window has an area of 169 square inches. How wide is the window?
So 169 = 13.
Pre-Algebra
3-8 Squares and Square Roots
The table will fit through the door.
Find the square root of 16 to find the width of the table. Use the positive square root; a negative length has no meaning.
Try This: Example 2
A square shaped kitchen table has an area of 16 square feet. Will it fit through a van door that has a 5 foot wide opening?
So the table is 4 feet wide, which is less than 5 feet.
16 = 4
Pre-Algebra
3-8 Squares and Square Roots
Additional Example 3: Evaluating Expressions Involving Square Roots
Evaluate the expression.
A. 3 36 + 7
Evaluate the square root.
Add.= 25
B. 21 – 5 + 9 Evaluate the expression under the square root symbol.
Evaluate the square root.
Multiply.= 18 + 7
= 4 + 9
= 13 Add.
3 36 + 7 = 3(6) + 7
21 – 5 + 9 = 16 + 9
Pre-Algebra
3-8 Squares and Square Roots
Try This: Example 3
Evaluate the expression.
A. 2 25 + 4
Evaluate the square root.
Add.= 10
B. 41 – 5 + 5Evaluate the expression under the square root symbol.Evaluate the square root.
Multiply.= 10 + 4
= 6 + 5= 11
Add.
2 25 + 4 = 2(5) + 4
41 – 5 + 5 = 36 + 5
Pre-Algebra
3-8 Squares and Square Roots
Lesson Quiz
Find the two square roots of each number.
1. 81 2. 2500
Evaluate each expression.
3. 3 16 + 1 4. 7 9 – 2 49
9 50
13 7
5. Ms. Estefan wants to put a fence around 3 sides of a square garden that has an area of 225 ft2. How much fencing does she need? 45 ft