Square Roots and Radical Expressions
Radical expressions and functions, square roots, notation, evaluating square roots, square root functions, simplifying forms, examples, and other roots. Learn how to evaluate, simplify, and understand square roots effectively.
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Chapter 7 section 1 Radical Expressions and Functions Page 502
Square Roots ( ) 2=25 The reverse operation of squaring a number is finding the square root of the number 52=25? ? ? ? ? ? ? ? and? ? ? ? ? ?-5 One square root of 25 is 5 because Another square root of 25 is -5 because 52=25 -5 ( ) 2=25 If , then b is a square root of a b2=a
Notation Radical sign denote the positive or principal square root of a number Number under the radical sign , 6 is called the radicand. Number between the v in the radical sign is the root index. In this example, it is a 3. The root index is not written when it is a 2. Symbol denote the negative square root of a number Example: = -5 since and -5 is negative. - 25 6 3 6 - -5 ( ) 2=25
Evaluate Square Roots Evaluate and explain your answer: 1) 81 2) - 36 36+64 3) 36+ 64 4)
Square Root Function f(x) = x If x is a negative number . . . What is the domain of: f(x) = What does the graph look like? x
Evaluating Square Root Functions If f(x) = find f(2) 3x+2
Simplifying the form Notice: a2 And 42= 16 =4 ) ( 2= 16 =4 -? 4 So to simplify expression of the form, Any real number a, = |a | The principal square foot of a2is the absolute value of a a2 a2
Example -6 ( ) 2 solution |-6| 6 ( ) 2 x+5 Solution |x + 5 |
Other roots =b? ? ? ? means? that? b3=a 3 a =b? ? ? ? means? that? b5=a 5 a
Example 3 -64x3 Solution 3 -64x3 ( ) 3 -? 4x 3 - 4x
Try a) -27 3 5x-3 ( ) 3 3 b)
Example Even ( ) 4 x-3 4 Solution |x 3 | Odd ( ) 5 2x+7 5 Solution 2x + 7
Try c) 3 -8x3 -6 ( ) 6 6 d) e) 5 -32x5
Try f) Find g(2) if g(x) = 8x-8 3
