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Notes 3/18
11-1 Real Numbers
CA Standard 2.0: Understand and use the operation of taking a root.
Vocab:
square root:__________________________________________________
principal square root:___________________________________________
radical sign:__________________________________________________
real numbers:_________________________________________________
rational number:_______________________________________________
irrational number:______________________________________________
inverse operations:____________________________________________
Ex 2) Simplify  36
Ex 1) Simplify 625
Approximate each square root to the nearest thousandth. Use table on page 648
Ex 3) 54
Ex 4) 93
Classify each number as rational or irrational. If it is rational, further classify it as
a whole number, an integer, or a rational number.
Ex 5) 125
Ex 6) 0.25
Homework: page 485 #16-36 even, #37-40 all
Ex 7)  1
Notes 3/19
11-2 Radical Expressions
CA Standard 2.0: Understand and use the operation of taking a root
Vocab:
radical expression:_____________________________________________
radicand:____________________________________________________
IMPORTANT: when taking the square root of a perfect square variable (like x6),
use the absolute value of the square root (if it is an odd exponent) since it MUST
be positive (like |x3|)
Simplify:
Ex 1) (5 x) 2
Ex 2) 16x10
Ex 3) 225n12
Ex 4)
x 2  8x  16
Solve:
Ex 5)  x 2  3
Ex 6)
x 2  6x  9  5
Homework: page 489 #18-42 even
Notes 3/20
11-3 Simplifying Radical Expressions and Cube Roots
CA Standard 2.0: Understand and use the operation of taking a root
Vocab:
cube root:____________________________________________________
Product Property for Radicals:
For any nonnegative real numbers a and b,
Ex:
ab  a  b
1225  25  49  25  49  5  7  35
*note: from now on, we assume variables are non-negative, so we no longer
need to use the absolute values
Simplify:
Ex 1) 16x 3
Ex 2) 125a 9
Ex 3) 144(n  3) 8
Ex 4) 9 36 x 2 y 5
Ex 5) 3 125
Ex 6) 3  1000
Ex 7) 3  54 x 6 y 10
Homework: page 493, last column (#29, 32, 35, 38, 41, 44), #46-54 even
page 494 #2-16 even
Notes 3/21
11-4 Multiplying Radical Expressions, and Rational Exponents
CA Standard 2.0: Understand and use the operation of taking a root and raising to a fractional power.
Vocab:
rational exponent:____________________________________________
Product Property for Radicals:
For any nonnegative real numbers a and b,
a  b  ab
Simplify
Ex 1) 3  12
Ex 2) 3x  5x  2
Ex 3) 5x  20x 3
Ex 4)
Ex 5) 8
1
3
Ex 6)  343
1
3
5a11
7102 a 4
b 27


3
2
2
1
2
Ex 7) (25 ) 3
Homework: page 496 #38-52 even, and page 497 #2-10 even
Notes 3/22
11-5 Dividing and Simplifying
CA Standard 2.0: Understand and use the operation of taking a root and raising to a fractional power.
Vocab:
rationalize the denominator:_____________________________________
____________________________________________________________
Division Property for Radicals:
For any nonnegative real numbers a and b, where b  0,
a

b
a
and
b
a

b
a
b
Simplify:
Ex 1)
12
75
Ex 2)
40b 3
10b 2
Rationalize the denominator:
Ex 3)
3
2y
Ex 4)
27 z 3
6
Ex 6)
5
4
8
3
Simplify:
Ex 5)
3 6
6 2
Homework: page 501 #46-54 even, #56-72 every other even, #74-78 even