Asquare lawn has area 128128 ft squared .ft2. a sprinkler placed at the center of the lawn sprays water in a circular pattern that just covers the lawn. what is the radius of the circle?

For this case what you must do is find the diagonal of the square to find the diameter of the circle and then be able to obtain the radius.
 We have then:
 A = L ^ 2 = 128
 L = root (128)
 L = 11.3137085
 Then, the diagonal of the square knowing its sides is:
 d = root ((L) ^ 2 + (L) ^ 2)
 d = root ((11.3137085) ^ 2 + (11.3137085) ^ 2)
 d = 16 feet
 Finally the radius of the circle is:
 r = d / 2
 r = (16) / 2
 r = 8feet
 
 the radius of the circle is
 r = 8feet