Download √n the means the positive (or principal) square root of a number.

Section3.2_Perfect_Squares_Perfect_Cubes_And_Their_Factors.notebookNovember 01, 2015
Section 3.2: Perfect Squares (Review), Perfect Cubes (New) and Their Roots
A Perfect Square is the square of a whole number. It is any whole number that can be represented as the area of a square with a whole number side length. (A = lw)
36 is a perfect square because 6 x 6 = 36, or 62 = 36, this can be shown in a square . . . 6
So, the length of the side of the square can be represented by 36 is a perfect square and 6 is its square root.
You should know the first 20 perfect squares:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400
√n ­ the means the positive (or principal) square root of a number.
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Section3.2_Perfect_Squares_Perfect_Cubes_And_Their_Factors.notebookNovember 01, 2015
Finding Squares Roots of Whole Numbers Using Prime Factorization:
1) Write the number as a product of its prime factors.
2) Group the factors in pairs.
3) Rearrange the factors into 2 equal groups. The square root is the product of the factors in one of the equal groups.
Ex 1) Find the square root of the following using prime factorization.
A)
B)
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Section3.2_Perfect_Squares_Perfect_Cubes_And_Their_Factors.notebookNovember 01, 2015
Reminder
√n ­ the means the positive (or principal) square root of a number.
What is the square root of 4?
What is √4 ?
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Section3.2_Perfect_Squares_Perfect_Cubes_And_Their_Factors.notebookNovember 01, 2015
A Perfect Cube is the cube of a whole number. It is any whole number that can be represented as the volume of a cube with a whole number side length. (V = lwh)
(Multiplying a number by itself three times)
216 is a perfect cube and 6 is its cube root.
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Section3.2_Perfect_Squares_Perfect_Cubes_And_Their_Factors.notebookNovember 01, 2015
Symbol & Terminology
This means the cube root of 1728.
When there is no number in the radical the index is assumed to be 2. Ex) is the same as You should know the first 6 perfect cubes:
1, 8, 27, 64, 125, 216
Finding Cube Roots Using Prime Factorization:
1) Write the number as a product of its prime factors.
2) Group the factors in groups of three.
3) The cube root is the product of the factor triplets.
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Section3.2_Perfect_Squares_Perfect_Cubes_And_Their_Factors.notebookNovember 01, 2015
Example:
Evaluate (without a calc).
A)
B)
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Section3.2_Perfect_Squares_Perfect_Cubes_And_Their_Factors.notebookNovember 01, 2015
Example:
Compute the following using technology:
A)
D)
B)
C)
E)
What does each mean?
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Section3.2_Perfect_Squares_Perfect_Cubes_And_Their_Factors.notebookNovember 01, 2015
Example: Compute.
A)
B)
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Section3.2_Perfect_Squares_Perfect_Cubes_And_Their_Factors.notebookNovember 01, 2015
Applications of Square Roots and Cube Roots
Squares
A
s
A = s2
s = √A
s
Cubes
Volume V = s3
Surface Area
SA = 6s2
s = ∛V
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Section3.2_Perfect_Squares_Perfect_Cubes_And_Their_Factors.notebookNovember 01, 2015
Examples
1. What is the length of the side of a square farm which contains 1764 yd. 2? How far apart are its opposite corners? 2. A right rectangular prism measures 9 in. x 8 in. x 24 in. What are the dimensions of a cube with the same volume? 10
Section3.2_Perfect_Squares_Perfect_Cubes_And_Their_Factors.notebookNovember 01, 2015
3. If the volume of a cube is 125m3, what is the surface area of the cube? 4. The surface area of a cube is 1176 cm2. What is the volume of the cube?
Assign pages 146­147 #’s 4, 5, 7­10
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Section3.2_Perfect_Squares_Perfect_Cubes_And_Their_Factors.notebookNovember 01, 2015
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Section3.2_Perfect_Squares_Perfect_Cubes_And_Their_Factors.notebookNovember 01, 2015
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