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7.1 Radical Expressions

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**Objective 1: Find principal square roots of numbers**

A square root of a number a is a number c such that Examples: 25 has a square root of 5 because 25 has a square root of -5 because -16 does not have a real-number square root because there is no real number c such that

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Theorem 7-1 -Every positive real number has two real-number square roots. -The number 0 has just one square root, 0 itself. -Negative numbers do not have real-number square roots. Ex. Find the two square roots of 64. The square roots are 8 and -8.

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Try This Find the square roots of each number. 9 36 121 -49

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Definition The principal square root of a nonnegative number is its nonnegative square root. The symbol represents the principal square root of a. the negative square root of a is written . Ex. Simplify

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Try This Simplify

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Definition The symbol is a radical sign. An expression written with a radical sign is a radical expression. The expression written under the radical sign is the radicand.

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Theorem 7-2 For any real number a, . The principal (nonnegative) square root of is the absolute value of a. Ex

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Try This

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**Objective 2: Find odd and even kth roots**

The number c is the cube root of a if 2 is the cube root of 8 because -5 is the cube root of -125 because Ex. Simplify.

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Try This Simplify

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**Rewrite using exponential notation**

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Try This

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**The number k in is called the index**

The number k in is called the index. If k is an odd number, we say that we are finding an odd root. Examples. Find the following

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Try This Find the following

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**Theorem 7-3 For any real number a, the following statements are true.**

A When k is even. B. When k is odd.

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Try This Find the following

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