Expressions and equations involving radicals
84 RadDeriv This program leads the student through the derivation of the Pythagorean Theorem via equations describing the areas of squares and triangles. Students should be encouraged to modify the original right triangle using the right (or left) cursor keys, to emphasize that the derivation holds for any right triangle. It should not be too difficult for students who are nearing the end of the term, though they may have to be coached about the figure representing C². The program does not keep track of errors. Completion warrants 100. This program and the next can probably be done in one 90-minute block.
85 RadPythg The program, Radical expressions: Pythagorean theorem, requires that the student observe the length of two sides of a right triangle and calculate the length of the hypotenuse. It also asks for the perimeter and area of the triangle. In specifying the perimeter, the student should use the radical expression for the hypotenuse (unless it turns out to be a perfect square). The program is looking for the exact answer, which can only be expressed with the radical (or a fractional exponent, which is also accepted).
86 RadDstnc In the program, Radical expressions: Distance Between Two Points, the program is expecting an exact answer, so the radical symbol will have to be used. The program also asks for the X and Y coordinates of the midpoint of the line segment between the two points. This, of course, is simply the average of the X coordinates and of the Y coordinates, respectively. The program alternates between representing the two points graphically and by means of coordinate ordered pairs.
87 RadNmrc1 This program focuses on multiplying and adding terms that contain the square root radical. It also deals with determining the distance between two points whose locations are specified in functional notation.
88 RadNmrc2 This program focuses on division and multiplication of radicals with emphasis on removing radicals from the denominator of an expression.
89 RadExprs This program focuses on simplifying expressions containing variables under the radical.
90 RadEqua The task in this program is to solve equations containing radicals. As indicated on the screens, the answers may be fractional, in which case it is safest to use a common fraction because exact answers are required. Rounding a decimal, such as .333 for 1/3, will not work. In some cases there is no solution because the radical indicates the positive branch, which, therefore, cannot be equal to a negative number. Indicate that fact with the letter [N].