Unformatted text preview: ecimal,
the denominator cannot contain a radical.
examples: Simplify
30
6 = 30
6 = 5 18
75 6
25 = b) = 6
25 = a) 6
5 or 16
5 When the denominator of a fraction is an irrational number, the denominator is a nonterminating and nonrepeating number. It is impossible to divide by such a decimal
number. The process or rewriting a fraction so that the denominator is not irrational is
called rationalizing the denominator.
examples: Simplify
a) 5
7 = =
= 5 7 (5)(7)
(7)(7)
35
7 7 7 = b) 15
20 = 15
25 15 = 2 5 15 5
= 2 (5)(5) 1 35
7 15 5
10
35
=
2 5 5 = exercises: Simplify
56
a)
2 11 5 66
22 b) 57
2 90 70
12 c) 5
34 = 35
2 53 2
2 Unit 4: Day 3 notes  Dividing Radical Expressions Page 2 of 2 CONJUGATES
The conjugate of a binomial is another binomial with the same first term, but the
second term has the opposite coefficient (opposite sign); a + b and a − b .
The product of conjugates (a + b)(a −b) is a2 − b2 .
example: Multiply ( 7 3 − 2 5 ) to its conjugate. (7 3 − 2 5 ) (7 3 + 2 5 ) (7 3) 2 (2 −
−
127 147
Answer: 5) 2 20 Note that the product of binomial radical conjugates is a rational number. DIVIDING RADICAL EXPRESSIONS
Consider the division 6 ÷ (1 + 5 ) ; this division results in the quotient 6
1+ 5 This fraction is not in simplest form because there is a radical in the denominator.
example: Simplify 6
1+ 6
1+ 5 6 (1 − o Use the conjugate to simplify (1 + 5 5) 5 ) (1 − 6 (1 − 5) 5) (1)2 − ( 5 ) 2 6 (1 − 5 )
−4
− 3 (1 − 5 )
2 Answer: exercise: Simplify −3+3 5
2 2 3 −3 2
2 3 +3 2 = − 33
+
5
22 [Answer: −5 + 2 6 PRECALCULUS 11 Unit 4 – Day 4: RADICAL EQUATIONS (Part 1) RADICAL EQUATIONS
A radical equation is an equation having radicals with the variable in the radicand.
The solution of any equation are all values of the variable that satisfies the equation.
9− x + 5 = 2 is an example of a radical equation. Since there is a square root of a variable expression, there may be restrictions from the radicand: x + 5 ≥ 0 ∴ x ≥ −5
This equation can be solved graphically:
• Rewrite the equation so that one side is 0; graph y = (the nonzero side); the roots
are the xintercepts.
• Graph y = (the left side) and y = (the right side); the roots ar...
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 Fall '11
 Aytona
 Calculus, PreCalculus, Radicals

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