Download - Geometry/Notes before 7
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Radical Expressions
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Operations on Radical Expressions• How can I simplify radical expressions?• How can I preform mathematical operations on
radical expressions?• How can I find the Geometric Mean between two
numbers?
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Radical Expressions• Radical = square root symbol
• Perfect squares – multiply two numbers by themselves
• But life isn’t always perfect!
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Radicals• Radical Expressions – an expression with a square
root
• Radicand – the expression under the radical sign
• We are going to simplify
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Product Property• so….• If you just have a number under the square root• Step 1 – find the prime factorization of the number• Step 2 – find pairs of the same number• Step 3 – put the one from each pair in front of the radical
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Radicands with numbers• Simplify:
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Adding and Subtracting Radical Expressions• The radicand must be the same.
• Which expressions can be added to 3?
• 10• 10
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Adding/Subtracting
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Unlike Radicands• Simplify the radicands to see if they have like
radicands
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Multiplying Radicals
• Step 1 – multiply the numbers• Step 2 – put the results under a square root• Step 3 – simplify as before
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Multiplying Radicals• You can only multiply inside numbers with inside
numbers and outside numbers with outside numbers
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Homework• Radical Quiz Friday!
• Worksheet
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Quotient Property• so…
• but…
• NO RADICALS IN THE DENOMINATOR!
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Rationalizing the Denominator
• Step 1 – multiply both the top and bottom of the fraction by the bottom
• Step 2 – the denominator will now be the number without a radical sign
• Step 3 – simplify the numerator, if possible
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Rationalizing the Denominator• Simplify:
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Geometric Mean• Geometric Mean – The geometric mean between
two numbers is the positive square root of their product.
• The two numbers are a and b, x is the geometric mean
• Use cross products and square roots
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Examples• Find the geometric mean between each pair of
numbers:
1. 4 and 4
2. 4 and 63. 6 and 94. ½ and 2
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Examples
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Given the mean
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Homework
• Worksheet• Radical Quiz Friday!