Reducing Radicals on the TI-86 (85)

This page presents and then demonstrates the use of a TI-86 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-85 and TI-86

click here to download tostr.85p
click here to download tostr.86p

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-85 and TI-86 Part 1	Part 2

click here to download rdcroot.85p	click here to download rdcroot.86p

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 actual menu appears at the bottom. We would like to open the NAMES submenu. Therefore, to leave Figure 1 and move to Figure 2 we will press the key.
Figure 2 Figure 2 shows the NAMES submenu for this calculator. In this case there are only three programs on this calculator. The menu does not have room to give the entire name for each program. Rather, the menu lists abbreviations for the programs. We are interested in the RDCROOT program which is abbreviated to RDCRO. We press to select that option, and move to Figure 3.
Figure 3 The result of selecting the RDCRO (F3) in Figure 2 is that the full name of the program, RDCROOT, has been pasted to the screen in Figure 3. We could have achieved the same result by using the alphabetic keys to type each of the letters in the program name. However, using the menu is usually shorter and less error prone.
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.

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 to reduce. Note that we do not get a chance to change the index value. The program only asks for the index once at the start of the program.
Figure 6 Figure 6 demonstrates having the calculator program reduce . The program is still doing square roots. All we needed to do was to 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 number.
Figure 7 What if we want to find ? We need to stop the program and then restart it, specify the index as 3, and then go on with the problem. We stop the program by interrupting it with the key. The result is given in Figure 7.
Here we have only two options. We can GOTO the interrupted line in the program, which we do not want to do, or we can QUIT which we do want to do. Therefore, we can leave Figure 7 by pressing the key.

Figure 8 We can recall the last command that we gave to the calculator by pressing the keys. Our last command was the RDCROOT command from Figure 3. Figure 8 demonstrates the recall of that command via those keys.
Once recalled, we can perform the command, that is, start the program, by pressing the key.
Figure 9 In Figure 9 we have told the program to find the cube root of ^–54.
Figure 10 Press to accept the last value in Figure 9 and allow the program to produce the result shown in Figure 10. Here the calculator indicates that the answer is negative 3 times the cube root of 2.
Figure 11 Figure 11 completes the demonstration by showing the calculator work for finding that the cube root of 10080 is 2 times the cube root of 1260.

Figure 1	Figure 1 shows the calculator screen after we have pressed the key to open the PROGRAM menu. The actual menu appears at the bottom. We would like to open the NAMES submenu. Therefore, to leave Figure 1 and move to Figure 2 we will press the key.
Figure 2	Figure 2 shows the NAMES submenu for this calculator. In this case there are only three programs on this calculator. The menu does not have room to give the entire name for each program. Rather, the menu lists abbreviations for the programs. We are interested in the RDCROOT program which is abbreviated to RDCRO. We press to select that option, and move to Figure 3.
Figure 3	The result of selecting the RDCRO (F3) in Figure 2 is that the full name of the program, RDCROOT, has been pasted to the screen in Figure 3. We could have achieved the same result by using the alphabetic keys to type each of the letters in the program name. However, using the menu is usually shorter and less error prone. 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.
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 to reduce. Note that we do not get a chance to change the index value. The program only asks for the index once at the start of the program.
Figure 6	Figure 6 demonstrates having the calculator program reduce . The program is still doing square roots. All we needed to do was to 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 number.
Figure 7	What if we want to find ? We need to stop the program and then restart it, specify the index as 3, and then go on with the problem. We stop the program by interrupting it with the key. The result is given in Figure 7. Here we have only two options. We can GOTO the interrupted line in the program, which we do not want to do, or we can QUIT which we do want to do. Therefore, we can leave Figure 7 by pressing the key.
Figure 8	We can recall the last command that we gave to the calculator by pressing the keys. Our last command was the RDCROOT command from Figure 3. Figure 8 demonstrates the recall of that command via those keys. Once recalled, we can perform the command, that is, start the program, by pressing the key.
Figure 9	In Figure 9 we have told the program to find the cube root of ^–54.
Figure 10	Press to accept the last value in Figure 9 and allow the program to produce the result shown in Figure 10. Here the calculator indicates that the answer is negative 3 times the cube root of 2.
Figure 11	Figure 11 completes the demonstration by showing the calculator work for finding that the cube root of 10080 is 2 times the cube root of 1260.