Finding Square Roots a number a is a

Finding Square Roots -a number a is a square root of b if a 2 = b Example: 42 = 16 and (-4)2 = 16, so 4 and -4 are square roots of 16 -a radical symbol indicates a square root. The expression under the radical sign is a radicand. Example 1: Simplify the following square roots. a. ) c. ) =8 = -3/5 b. ) d. ) = Is undefined

-Some square roots are rational numbers and some are irrational. Example: Rational Irrational -1. 2, 9, 2/3 . 57734…, -2. 1348274… Example 2: Tell whether each expression is rational or irrational. a. ) b. ) irrational Estimating Square Roots -The squares of integers are called perfect squares. Consecutive Integers: 1 2 3 4 5 6 7 Perfect Squares: 4 9 16 25 36 49 1 -You can estimate square roots by using perfect squares.

Example 3: Estimate the following square roots by asking yourself which two perfect squares is the radicand in between. Between what two consecutive integers are the following. a. ) b. ) 14. 52 is between the two perfect squares 9 and 16 105 is between the two perfect squares 100 and 121 Therefore, Is between 3 and 4 Is between -10 and -11

Example 4: Approximate the following square roots using a calculator. a. ) b. ) = 4. 22 = -14. 25

Factoring Square Roots Factoring square roots is just like factoring any integer, but our goal is to find factors that are perfect squares. Example of Factoring an Integer 24 = 8 x 3 So 24 = 2 x 2 x 3 4 x 2 2 x 2 Example of Factoring a Square Root So,

Example 5 - Factor these square roots into simplest form. a. ) b. )