6.1 Notes KEY
9Algebra 2Name: Ms. Fisher
6.1 Day 1 NotesDate: March Pd: 9
6.1 – Roots of Real Numbers
Warm-up:
Simplify
1. = 82. = 5.193. = 3
8*8 = 64
4. = 15. = -36. = 3 (5.19) = 15.58
LESSON
I. Square Roots
A. What is a Square Root?!
Square Root: ___a divisor of the quantity that when squared gives the quantity. Ex: = 8 and 8² = 64
***Every positive number has twosquare roots: positive and negative
Example:
The square roots of 16 are: = + 4 or -4
4 x 4 = 16 and -4 x -4 = 16
Principal Square Root: the non-negative positive square root. 4
*** NOTE: A negative number b has NO real Square Root!
Find the square root of each number. If it does not represent a real number, say so. TEACHER DO
a. = +/-3b. c. d. = 0.3 e.
3x 3=9 no a real # 0.3 *0.3 = 0.09 9
=a³
II. Cube Roots
Cube Root: a number that produces a specified number when it is multiplied by itself three times.
***Every number has ONEcube root.
TEACHER DO
Examples:
a. b. c. d. e.
+/- 4 no real number 2 -2 = 5ab
2*2*2=8 -2*-2*-2=-8
STUDENTS DO:
Simplify:
a. b. c. d. e.
3 -3
= 3a 10² 10²
III. nth Roots
We can actually take an nth root of a number b. It is a solution to the equation xn = b
Radical Notation:
If our index, n, is even:
1. If b is positive, then there are ______TWO______real nth roots.
The principal nth root, denoted
The other root is
2. If b = 0, there is ______ONE______root. i.e.
3. If b is negative, then there are ____NO______real roots of b.
If our index, n, is odd:
1. There is ____ONE______real nth root of bwhether b is positive, negative, or zero.
Properties of Radicals: / Examples1. / = 2 = 2 = -2
2. / = │2│ means JUST the POSITIVE 2
TEACHER DO
Simplify. If the expression does not represent a real number, say so.
1. 2. 3. 4. 5. Factor Tree -3 │-8│= 8 -8
125
5 25 -3*-3*-3= -27
5 5
Final Answer =
5³ 2
STUDENTS DO
6. 7. 8. 9. 10.
Factor Tree Factor Tree │ -5│= 5 -5
400 81 10²
10 40 9 9 neg * neg =turns pos neg*neg*neg-stays neg
2 5 4 10 3 3 3 3
2 2 2 5
5*2=10*2=20 │3│= 3
5*2= 10*2= 20
20 *20 =400
Final Answer: 20
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