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Transcript
VOCABULARY UNIT 4 SECTION 1:
1. Real number : the set of all numbers that can be expressed as a decimal
or that are on the number line. Real numbers have certain properties and
different classifications, including natural, whole, integers, rational and
irrational.
2. Irrational number- real numbers that cannot be represented as
terminating or repeating decimals. Example ∏, e, √2
3. Rational number: A number expressible in the form a/b or – a/b for
some fraction a/b. The rational numbers include the integers.
4. Natural numbers: 1,2,3,4,...
5. Whole numbers. The numbers 0, 1, 2, 3, ….
6.Integers: …,-3,-2,-1,0,1,2,3,…
VOCABULARY CONTINUED
7. Nth roots: The number that must be multiplied by itself n times to equal a
given value. The nth root can be notated with radicals and indices or with
rational exponents, i.e. x1/3 means the cube root of x.
8. Base: The number that is going to be raised to a power.
9. Exponent (power): A number placed above and to the right of another
number to show that it has been raised to a power.
10. Index: The number outside the radical symbol.
11. Radicand: is the number found inside a radical symbol, and it is the
number you want to find the root of
12. Radical: An expression that uses a root, such as square root, cube root.
13. Rational exponent : For a > 0, and integers m and n, with n > 0, ; am/n =
(a1/n)m = (am)1/n .
Section 1: Review of number systems/
Radicals and rational Exponents
ESSENTIAL QUESTION:
How are rational exponents and roots of expressions
similar?



Extend the properties of exponents to rational
exponents.
MCC9-12.N.RN.1 Explain how the definition
of the meaning of rational exponents follows
from extending the properties of integer
exponents to those values, allowing for a
notation for radicals in terms of rational
exponents
MCC9-12.N.RN.2 Rewrite expressions
involving radicals and rational exponents
using the properties of exponents.
Number systems review
Radicals and
Rational Exponents
Radical Notation
n is called the index number
a is called the radicand
Let’s say you have
63 = 216
this is in exponential notation
put this in radical notation:
Properties of Radicals
Simplifying Radicals
1. The radicand has no factor raised to a power
greater than or equal to the index number.
2. The radicand has no fractions.
3. No denominator contains a radical.
4. All indicated operations have been performed
Simplifying Radicals
• If there is no index #, it is understood to be
2
• Use factor trees to break a number into its
prime factors
• Apply the properties of radicals and
exponents
Simplifying Radicals
Simplifying radical expressions
Example
1.
2.
3.
Examples of simplifying Radical Expressions
1.
2.
Rational Exponents- When the exponent can be
expressed as m/n where m and n are integers and n
cannot equal zero
81/3 =
163/4 =
16 -1/3
=2
=
=
Writing Expressions in radical form
1. 642/3
2. (-8)5/3
Writing expressions with rational exponents
1.
2.
Multiplying
Radicals
1. Radicals must have the same index
number
2. Multiply outsides and insides together
3. Add exponents when multiplying
4. Simplify your expression
5. Combine all like terms
Assume that all variables represent
nonnegative real numbers.
Assume that all variables represent
nonnegative real numbers.
Dividing Radicals
1.No radicals in the denominator
2.No fractions under the radicand
3.Apply the properties of radicals
and exponents
Assume that all variables represent
nonnegative real numbers and that
no denominators are zero.
Assume that all variables represent
nonnegative real numbers and that
no denominators are zero.
Assume that all variables represent
nonnegative real numbers and that
no denominators are zero.
Assume that all variables represent
nonnegative real numbers and that
no denominators are zero.
Simplifying each expression. Express your
answer so that only positive exponents
occur. Assume that the variables are
positive.
Simplifying each expression. Express your
answer so that only positive exponents
occur. Assume that the variables are
positive.
Simplifying each expression. Express your
answer so that only positive exponents
occur. Assume that the variables are
positive.
Homework:
Worksheet 4-1 and 4-2
homework- P 451 # 1-3, 9, 13-19, 25- 28, 37-40
Coach book: Pages 174-175 # 1-15