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Section 9.1: Evaluating Radical Expressions and Graphing Square Root and Cube Root Functions

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9.1 Lecture Guide: Evaluating Radical Expressions and Graphing Square Root and Cube Root Functions

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The natural number n is the index or the order of the radical. Radical Notation denotes the principal nth root of x x is the radicand. is the radical symbol, or the radical. The natural number n is the index or the order of the radical.

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Principal Square Root Algebraically Verbally Numerically For any real number : if and denotes the principal square root of x. Graphically by

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Principal Cube Root Algebraically Verbally Numerically For any real number x: Graphically if y is a real number and denotes the principal cube root of x. by

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Objective: Evaluate radical expressions.

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Evaluate each expression. Use a calculator only to check your answer. 1. 2.

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Evaluate each expression. Use a calculator only to check your answer. 3. 4.

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Evaluate each expression. Use a calculator only to check your answer. 5. 6.

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Evaluate each expression. Use a calculator only to check your answer. 7.

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Evaluate each expression. Use a calculator only to check your answer. 8.

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Evaluate each expression. Use a calculator only to check your answer. 9.

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Evaluate each expression. Use a calculator only to check your answer. 10.

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Objective: Graph square root and cube root functions.

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11. Type: x-intercept: y-intercept: Domain: Range: Table Graph

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12. Type: x-intercept: y-intercept: Domain: Range: Table Graph

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Objective: Determine the domain of a square root function.

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Domain of a Function The domain of a real-valued function set of all real numbers for which is the ____________________ ____________________ under a is also a real number. This means the domain excludes all values that cause division by ____________________ or cause a square root symbol.

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13.Determine the domain of using a calculator. Then graph without a window of using by to verify your result.

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14.Determine the domain of using a calculator. Then graph without a window of using by to verify your result.

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Determine the domain of the following. Use a graphing calculator only as a check on your work. 15.

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Determine the domain of the following. Use a graphing calculator only as a check on your work. 16.

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Determine the domain of the following. Use a graphing calculator only as a check on your work. 17.

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Determine the domain of the following. Use a graphing calculator only as a check on your work. 18.

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19.Givenevaluate each expression without a calculator.

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