9.1 To evaluate square roots Objective Part I Evaluating Square Roots

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Presentation transcript:

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.

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

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

 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:  2.236068… 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.

Example 2 Irrational Evaluate the expression. a. b. c. d. 7 is NOT a perfect square

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

Example 4 Evaluate the expression. Expression represents two numbers