Section 11.1 11.1 The Square Root Property Remember:  Every positive number has 2 square roots – a positive one and a negative one.  Squaring and taking the square root are opposite operations and “undo” each other. 64 has both a positive and a negative square root Example 1: x 2  64
The square root of x2 is x. x 2   64 x  8
Remember: Radials need to be simplified! Example 2: x 2  18
x 2   18
x 9 2
x  3 2
Example 3: You need to solve for both the positive and the negative square root. ( x  4) 2  9
( x  4) 2   9
x  4  3
x  4  3 | x  4  3
x  7 | x  1
Section 11.1 Example 4: (3x  4) 2  18
(3 x  4) 2   18
3 x  4  3 2
3 x  4  3 2
For MML you have to write 2 separate answers. 4  3 2
x
3
x
4  3 2
,
3
4  3 2
3
Remember: Don’t forget about imaginary numbers! Example 5: ( x  7) 2  36
( x  7) 2   36
x  7  6i
x  7  6i
For MML you have to write 2 separate answers. x  7  6i,  7  6i
Example 6: ( x  9) 2  12
( x  9) 2   12
x  9  2i 3
x  9  2i 3
x  9  2 3i,
 9  2 3i
For MML you have to write 2 separate answers and they probably want the i last.