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3.0 Radicals.notebook
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AN2 - Operations on radicals and radical expressions with numerical and variable radicands.
New outcome : Algebra and Number
radical
radicand
index restriction
like radicalssimilar to polynomials
.
Entire Radicals
Mixed Radicals
Converting Entire radicals to Mixed radicals
Perfect Squares
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Convert the following to mixed radicals.
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Convert the following from Mixed to Entire
.
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Write as a mixed radical.
.Page 2789 #2,3,4, 5, 6
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Order the following radicals from least to greatest.
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Adding and Subtracting Radicals
• you must have like radicals to add and subtract radicals
ex.
ex2.
Page 279#6,8,9, 10
Page 279 #11,13,14,15,16,19, 20
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Multiplying Radicals
-Radicand to radicand-coefficient to coefficient
.
page 289 #1a-d, 2, 3ab, 4abc 5a
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Dividing Radicals
* Divide coefficents if possible
* Divide radicands if possible
1. 2.
3.
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4.
p 290 #6,7
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We do not want to have radicals in the denominator
We need to rationalize the denominator to eliminate the radical
.
a)
b)
c)
d)
page 290 #8, 15
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More Multiplying...
a)
b)
c)
d)
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Multiplying by conjugate...
Conjugate: two binomial factors whose product is a difference of squares.(In one binomial there is a + and the other a -)
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Rationalize using conjugates...Rationalize the denominator!
.
You try....
b)
a)
page 290 #9, 10, 11, 13
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AN3 - Solving Problems that involve radical equations
When solving radical equations, always state restrictions first
Verify all solutions in the original equation to check for extraneous roots
→ Isolate the radical
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State the restrictions...
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Ex 2
Page 300 #,2,3,4
Solve:
An extraneous root is a solution found when solving algebraically that is found not to be a solution when checking the result by substitution.
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Solve
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Solve
page 300301 #5,6ab,7abd, 8bc, 10ab
page 3012
#11, 12, 13, 14, 15, 18, 19
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Rational Exponents
First, what is a rational number?
A rational number is a number that can be written as a ratio of two integers.
a where a and b are integers b
Two types of rational numbers
Terminating decimals
Repeating decimals
Rational Exponents
First, what is a rational number?
A rational number is a number that can be written as a ratio of two integers.
a where a and b are integers b
Two types of rational numbers
Terminating decimals
Repeating decimals
.
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Rational exponents:
Rational exponents are exponents that are rational numbers, rather self-explanatory, right?
Ex's
There is another way to express a rational exponent, using radicals. The most common radical is the square root.
=
.
In general there are two types of rational exponents:
Simple Roots, where:
When the denominator is 2 we have b ½ = = , the square root, where we normally don't write the 2. When the denominator is 3, we have = which is referred to as the cube root.
Complex roots where:
Convert to radical form:
Convert to exponent form:
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