Slide 1 : Lesson Presentation Lesson Quiz Warm Up
Slide 2 : Warm Up
Simplify each expression.
1. 62 36 2. 112 121 3. (–9)(–9) 81 4. 25
36 Write each fraction as a decimal. 5. 6. 7. 8. 0.4 5.375 0.5 –1.83
Slide 3 : Evaluate expressions containing square roots.
Classify numbers within the real number system. Objectives
Slide 4 : square root terminating decimal
perfect square repeating decimal
real numbers irrational numbers
natural numbers
whole numbers
integers
rational numbers Vocabulary
Slide 5 : 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 square
root are inverse operations. The radical symbol , is used to represent square roots. Positive real numbers have two
square roots. 4 ? 4 = 42 = 16 = 4 Positive square
root of 16 (–4)(–4) = (–4)2 = 16 = –4 Negative square
root of 16 –
Slide 6 : A perfect square is a number whose positive square root is a whole number. Some examples of perfect squares are shown in the table. 0 02 1 12 100 4 22 9 32 16 42 25 52 36 62 49 72 64 82 81 92 102 The nonnegative square root is represented by . The negative square root is represented by – .
Slide 7 :
Slide 8 : Example 1: Finding Square Roots of
Perfect Squares Find each square root. 42 = 16 32 = 9 Think: What number squared equals 16? Positive square root positive 4. Think: What is the opposite of the
square root of 9? Negative square root negative 3.
Slide 9 : Find the square root. Example 1C: Finding Square Roots of
Perfect Squares
Slide 10 : Find the square root. Check It Out! Example 1 22 = 4 Think: What number squared
equals 4? 52 = 25 Think: What is the opposite of the square root of 25?
Slide 11 : The square roots of many numbers like , are not whole numbers. A calculator can approximate the value of as 3.872983346... Without a calculator, you can use square roots of perfect squares to help estimate the square roots of other numbers.
Slide 12 : Example 2: Problem-Solving Application As part of her art project, Shonda will
need to make a square covered in glitter.
Her tube of glitter covers 13 square
inches. What is the greatest side length
Shonda’s square can have? The answer will be the side length of the
square. List the important information: • The tube of glitter can cover an area of 13 square inches.
Slide 13 : Example 2 Continued
Slide 14 : Example 2 Continued
Slide 15 : Guess 3.6: 3.62 = 12.96 too low Guess 3.7: 3.72 = 13.69 too high Example 2 Continued 3.6 3.7 4 3
Slide 16 : A square with a side length of 3.6 inches
would have an area of 12.96 square inches.
Because 12.96 is close to 13, 3.6 inches
is a reasonable estimate. Example 2 Continued
Slide 17 : What 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? Check It Out! Example 2 Guess 6.2 6.22 = 38.44 too high Guess 6.1 6.12 = 37.21 too low A square garden with a side length of 6.2 ft would have an area of 38.44 ft2. 38.44 ft is close to 38, so 6.2 is a reasonable answer.
Slide 18 : All numbers that can be represented on a number line are called real numbers and can be classified according to their characteristics.
Slide 19 : 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, …
Slide 20 : Terminating decimals are rational numbers in
decimal form that have a finite number of digits:
1.5, 2.75, 4.0
Slide 21 : Example 3: Classifying Real Numbers Write all classifications that apply to each
Real number. A. –32 –32 = – = –32.0 32
1 32 can be written as a fraction and a decimal. rational number, integer, terminating decimal B. 5 5 = = 5.0 5
1 5 can be written as a fraction and a decimal. rational number, integer, whole number, natural
number, terminating decimal
Slide 22 : Write all classifications that apply to each real number. rational number, repeating decimal 3b. –12 rational number, terminating decimal, integer irrational number Check It Out! Example 3 -12 can be written as a fraction and a decimal. The digits continue with no pattern.
Slide 23 : Find each square root. 1. 2. 3. 4. 12 -8 3
7 – 1
2 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 an
inch. 8.2 in. Lesson Quiz Write all classifications that apply to each real number. 6. 1 8. rational, integer, whole number, natural number, terminating decimal rational, repeating decimal irrational