Chapter 7 Radicals, Radical Functions, and Rational Exponents
How are Exponents related to Radicals?
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Transcript of How are Exponents related to Radicals?
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HOW ARE EXPONENTS RELATED TO RADICALS?
a1n= n√a
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VOCABULARYRadical SignRadical Expression
An expression that contains a radical sign.
Index A small number indicating the root or a radical expression
Radicand The number inside a radical sign
Prime Number
A Prime Number can be divided evenly only by 1, or itself. And it must be a whole number greater than 1.
Factor Factors are numbers you can multiply together to get another number
Prime Factor
A factor that is a prime number
Prime Factorization
Finding the prime numbers that multiply together to make the original number.
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IDENTIFY THE RADICAND & INDEX FOR THE FOLLOWING EXPRESSIONS.
Radicand:
Index:
Radicand:
Index:
Radicand:
Index:
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SIMPLIFYING RADICALS WITH PRIME FACTORIZATION
Prime Factorizatio
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SIMPLIFYING RADICALS WITH PRIME FACTORIZATION
Prime Factorizatio
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SIMPLIFYING RADICALS WITH PRIME FACTORIZATION
Prime Factorizatio
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COMBINING LIKE RADICALSWe can add or subtract like radical expressions by adding or subtracting the coefficients. (Like radicals have the same index and radicand)
When adding or subtracting like radicals, the radicand does
not change.
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EXAMPLE 1: SIMPLIFY EXAMPLE 2: SIMPLIFY
11√5+4 √58 √10+ 5√4−2√10+7 5√ 4
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QUICK CHECK TIME!!
Get out
your
white
boards!!
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SIMPLIFY
√12
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SIMPLIFY
√50
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SIMPLIFY
√ 45
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SIMPLIFY
2√18
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SIMPLIFY
8 √28
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SIMPLIFY
−3 √1000
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SIMPLIFY
√16𝑛2
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SIMPLIFY
√20𝑛2
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SIMPLIFY
√ 49𝑛3
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SIMPLIFY
√25 𝑥2𝑦
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SIMPLIFY
√90 𝑥4 𝑦 2
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SIMPLIFY
√81 𝑥3 𝑦 2