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Unit 3: Algebra: Rational Exponents and Square Root Functions
3.1 – Evaluate nth Roots and Use Rational Exponents
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Georgia Performance Standards
MM3A2a Define and understand the properties of nth roots MM3A2b Extend properties of exponents to include rational exponents MM3A3d Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology
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Vocabulary For an integer n greater than 1, if bn = a, then b is an nth root of a. An nth root of a is written as 𝑛 𝑎 where n is the index of the radical. If n is odd, then a has one real root. If n is even, then a has two real nth roots if a > 0, one real nth root if a = 0, and no real nth roots if a < 0.
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Radicals and rational exponents
How can you write the root of an integer using an exponent? An nth root of x is written as 𝑛 𝑥 where n is the index of the radical. 𝑛 𝑥 Index Radicand
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Radial Review – Think trees
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Radial Review
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Radial Review Solve the Following: 30 100𝑥3 200
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Radial Review Solve the Following: 𝟐 * 𝟖 𝟓 * 𝟕 2 𝟐 * 3 𝟓𝟎 𝟑 𝟐 * 𝟑 𝟒
𝟐 * 𝟖 𝟓 * 𝟕 2 𝟐 * 3 𝟓𝟎 𝟑 𝟐 * 𝟑 𝟒 Solve the Following:. 𝟓𝟏𝟐𝐦𝟑 𝟏𝟒𝟕𝐦𝟑𝐧𝟑 -4 𝟏𝟗𝟐𝐱 -3 𝟐𝟒𝐚𝟒𝐛𝟐𝐜𝟑
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Evaluate (a) 95/2 and (b) 27-2/3
Rational Exponent Form 95/2 = (91/2)5 = 35 = 243 27-2/3 = /3 = 1 (27 1/3 )2 = = 1 9
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Evaluate (a) 95/2 and (b) 27-2/3
Radical Form 95/2 = ( 9 )5 = 35 = 243 27-2/3 = = = 1 9
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Using a calculator Calculator Steps:
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Solve equations using nth roots
Solve the equation: -2x6 = -1458 (x+2)5 = 35
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Solve equations using nth roots
Solve the equation. Round the result to two decimal places: x = 132 2x = 53 (x+3)4 = 362
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Try the following Page 112 1-6 7-9 16-20 25-33
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