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**9.1 To evaluate square roots Objective Part I Evaluating Square Roots**

Square Root of a Number If , then b is a square root of a. Example: If 32 = 9, then 3 is a square root of 9. All positive real numbers have two square roots: a positive square root (or principal square root) and a negative square root. Square roots are written with a radical symbol The number or expression inside a radical symbol is the radicand.

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**The positive and negative square roots**

Meaning Positive square root Negative square root The positive and negative square roots Symbol Example You may use the table on pg 811 to help find square roots

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**You may not have a negative radicand**

Example 1 Evaluate the expression. a. Positive square root b. Negative square root c. Square root of zero d. Two square roots e. No real square root You may not have a negative radicand

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** 2.236068… non ending not repeating**

Perfect squares: occur when a number is multiplied by itself. EX: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225 Rational numbers: can be written as a fraction EX: 4 = 3 An irrational number is a number that cannot be written as a fraction. They include all non ending non repeating decimals EX: … non ending not repeating The square roots of numbers that are not perfect squares are irrational numbers and must be written using the radical symbol or approximated.

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**Example 2 Irrational Evaluate the expression. a. b. c. d.**

7 is NOT a perfect square

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**Evaluate the expression when a = 1, b = –2, and c = –3 .**

Example 3 Evaluate the expression when a = 1, b = –2, and c = –3 . Substitute values

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Example 4 Evaluate the expression. Expression represents two numbers

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