Reducing Radicals on the TI-83

This page presents and then demonstrates the use of a TI-83 program called RDCROOT to reduce radicals involving integers. The program produces a "nice looking" output. In order to do this it uses another program, TOSTR, to do some formatting. Therefore, TOSTR must be present on a calculator in order to run RDCROOT.

The following table presents a listing of the TOSTR program.

Listing of the TOSTR program
Listing is valid for TI-83

click here to download tostr.83p

The RDCROOT program is a bit longer. The table below gives the listing of the RDCROOT program in two parts.

Listing of the RDCROOT program Listing is valid for TI-83
Part 1	Part 2

click here to download rcdroot.83p

The frames below give a demonstration of the use of the RDCROOT program.

Figure 1 Figure 1 shows the calculator screen after we have pressed the key to open the PROGRAM menu. The names of the programs on the calculator are listed on the screen. We want RDCROOT, but it is not on the list shown in Figure 1.
Figure 2 Figure 2 shows the program names after we have moved down the list by pressing the key many times. Note that the display shows that we have stopped with the highlight at the RDCROOT program name.
We move to Figure 3 by pressing the key to paste the name of the program, prefixed by "prgm", onto the screen.
Figure 3 Now that we have the name on the program on the screen, all that we need to do to start the program is to press the key to start the program.

Figure 4 We have pressed the ENTER key and the calculator responds by asking for some values. First, the calculator wants to know the index of the root in question. We will try to reduce Therefore, the index is 2 for the square root. We enter and then press to continue the program. Now the calculator wants to know the value under the radical, or in our example, 32. We press to produce the screen as shown in Figure 4.
Figure 5 In Figure 4 we set up the problem. We press to accept the last value and have the program continue working. The program actually computes the answer to be 4 times the square root of 2, and it gives those values as part of the "Ugly Answers". However, the program then goes on to produce a nicer looking answer, namely
Unfortunately, the calculator display gives the square root as "^(1/2)". This will facilitate doing other roots as well as doing the square root.
After giving that response the program is ready for a new value, starting with a new index.
Figure 6 Figure 6 demonstrates having the calculator program reduce . The program is told to do a square root by setting the value of the index to be 2. We give 10080 as the desired value and then press enter. The calculator responds with the ugly answers and then with the nicer looking output. The answer is 12 times the square root of 70.
The program then continues to ask for the next index value.
Figure 7 What if we want to find ? We need specify the index as 3, and then give the value as ^–54. This was done in Figure 7. The answer is shown as negative three times the cube root of 2.
Figure 8 In Figure 8 we look at the cube root of 10080. This time the answer comes back as 2 times the cube root of one thousand two hundred sixty.
Figure 9 At the end of Figure 8 the program was ready to do another problem. But, how do we get out of the program? The answer is that we need only press the key. That will interrupt the program and produce the screen shown in Figure 9. There we have two choices. We could do the "Goto" command, which will start the program editor and allow us to edit the program. This is an option that we DO NOT want to take. The other option, "Quit", will terminate the program and take us back to the normal screen. We select that Quit option by pressing the . Doing so will move us to the display in Figure 10.
Figure 10 The program has terminated in Figure 10. We are ready to do other work on the calculator.

Figure 1	Figure 1 shows the calculator screen after we have pressed the key to open the PROGRAM menu. The names of the programs on the calculator are listed on the screen. We want RDCROOT, but it is not on the list shown in Figure 1.
Figure 2	Figure 2 shows the program names after we have moved down the list by pressing the key many times. Note that the display shows that we have stopped with the highlight at the RDCROOT program name. We move to Figure 3 by pressing the key to paste the name of the program, prefixed by "prgm", onto the screen.
Figure 3	Now that we have the name on the program on the screen, all that we need to do to start the program is to press the key to start the program.
Figure 4	We have pressed the ENTER key and the calculator responds by asking for some values. First, the calculator wants to know the index of the root in question. We will try to reduce Therefore, the index is 2 for the square root. We enter and then press to continue the program. Now the calculator wants to know the value under the radical, or in our example, 32. We press to produce the screen as shown in Figure 4.
Figure 5	In Figure 4 we set up the problem. We press to accept the last value and have the program continue working. The program actually computes the answer to be 4 times the square root of 2, and it gives those values as part of the "Ugly Answers". However, the program then goes on to produce a nicer looking answer, namely Unfortunately, the calculator display gives the square root as "^(1/2)". This will facilitate doing other roots as well as doing the square root. After giving that response the program is ready for a new value, starting with a new index.
Figure 6	Figure 6 demonstrates having the calculator program reduce . The program is told to do a square root by setting the value of the index to be 2. We give 10080 as the desired value and then press enter. The calculator responds with the ugly answers and then with the nicer looking output. The answer is 12 times the square root of 70. The program then continues to ask for the next index value.
Figure 7	What if we want to find ? We need specify the index as 3, and then give the value as ^–54. This was done in Figure 7. The answer is shown as negative three times the cube root of 2.
Figure 8	In Figure 8 we look at the cube root of 10080. This time the answer comes back as 2 times the cube root of one thousand two hundred sixty.
Figure 9	At the end of Figure 8 the program was ready to do another problem. But, how do we get out of the program? The answer is that we need only press the key. That will interrupt the program and produce the screen shown in Figure 9. There we have two choices. We could do the "Goto" command, which will start the program editor and allow us to edit the program. This is an option that we DO NOT want to take. The other option, "Quit", will terminate the program and take us back to the normal screen. We select that Quit option by pressing the . Doing so will move us to the display in Figure 10.
Figure 10	The program has terminated in Figure 10. We are ready to do other work on the calculator.