Download Algebra II-B Unit 8: Day 1 Simplifying Square and Cube Roots Big

Algebra II-B
Unit 8: Day 1 Simplifying Square and Cube Roots
Big Ideas: Inverse operations “undo” each other.
Vocabulary is used to help with explanations, memory and with decision making.
Equivalent forms of an expression can be found by simplifying or expanding.
I. Perfect Squares and Cubes
To be proficient in square and cube roots, we need to recognize all types of each.
Numeric
One Term Perfect
Perfect Squares Squares
12  _____
( x) 2  ____
2 2  _____
( x 2 ) 2  ____
3 2  _____
Perfect Square
Numeric Perfect
One Term Perfect
Trinomials
( x  4) 2 
Cubes
Cubes
13  _____
( x) 3  ____
2 3  _____
( x 2 ) 3  ____
( x 3 ) 2  ____
33  _____
( x 3 ) 3  ____
4 2  _____
( x 4 ) 2  ____
4 3  _____
( x 4 ) 3  ____
5 2  _____
( x 5 ) 2  ____
5 3  _____
( x 5 ) 3  ____
6 2  _____
( x 6 ) 2  ____
6 3  _____
( x 6 ) 3  ____
7 2  _____
( x 7 ) 2  ____
7 3  _____
( x 7 ) 3  ____
8 2  _____
( x 8 ) 2  ____
( x 8 ) 3  ____
9 2  _____
( x 9 ) 2  ____
( x 9 ) 3  ____
10 2  _____
( x 10 ) 2  ____
(3 y  4) 2 
10 3  _____
( x 10 ) 3  ____
Topical Understanding #1 – Exponents on perfect squares and cubes
_____________________________________________________________________
_____________________________________________________________________
Topical Understanding #2 – Perfect Square Trinomials______________________
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II. Simplifying Square Roots
1. Just like we should remove all factors that are perfect square (or any factor that
appears in pairs) we should never leave an exponent inside that is greater than one.
Problem Set 1: Simplify
a.
b.
250
49 x12
25
c.
9x 9
x 2  12x  36
d.
2. There are all kinds of considerations involving the signs of the quantities inside the
square root and the answers we give.
Problem Set 2: Simplify. If the quantity is not a real number, write “NO REALS”.
a.
 64
 64
b.
x  72
c.
III. Cube Roots –
1. The cube root (k) of a number (N) is any solution to the equation: ___________
Topical Understanding #3 – Cube roots and positives and negatives________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
Problem Set 3: Simplify.
a.
3
64
b.
3
 27x 27
c.
3
40x 8
III. Formal Problem Solving – Special Right Triangles
A. 45-45-90 Right Triangles (half a square)
1. Use the Pythagorean Theorem to find side c. Give answer as a simplified radical.
c
3
45o
2. In general, the sides of a 45-45-90 right triangle are related by the formulas in the
diagram below.
x 2
x
45o
x
B. 30-60-90 Right Triangles (half an equilateral triangle)
1. Use the Pythagorean Theorem to find the altitude (AE) of the equilateral triangle
 EQU. Give the answer in simplest radical form.
E
6
o
U 60
A
Q
2. In general, the sides of a 30-60-90 right triangle are related by the formulas in the
diagram below.
2x
x 3
HW: p. 295 #1-23 odd
o
60
x
Name ________________________
Date ________________________
Unit 8 Day 1 Skills Practice
1. Circle the numbers or expressions that are prefect squares. Cross out those that are
not.
121
x6
x 25
25 x 2 y 2
- 49
200
2. Circle the numbers or expressions that are prefect cubes. Cross out those that are
not.
y 12
144
 125
8x 9
27
8
-1
Simplify. If the expressions do not represent real number, write “NO REALS”
3.
6.
3
108
4.
x10 y 15
5.
x10 y 15
7.
 64
8.
3
3
32
 64