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 Rational or not? (Posted on 2015-05-29)
If I enter the expression

```35+42âˆš2
```
into my graphing calculator and then ask it for the fractional (rational) equivalent it cannot do so. Since the number is irrational it displays the first few decimal digits:

```94.39696962
```
However, if I enter the expression

```55+42âˆš2
```
into the same graphing calculator and then ask it for the fractional equivalent it displays:
```37751
-----
330
```
But this second number I entered is clearly not rational either.

What's going on?

 No Solution Yet Submitted by Jer Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: solution | Comment 2 of 5 |
(In reply to solution by Charlie)

Incidentally I can only get TI-84 Plus Silver edition graphing calculators to do this.  Not the TI-83 or 84+, just the more expensive Silver Edition.

Several of my students have other brands of non-graphing scientific calculator: TI-30, Casio, Sharp.
I tried this on all of the calculators that have a rationalize key and none of them made this error.

Add that to the criticism of the over-priced TI graphing calculators.

I'm just finding out this goes further than I thought:
You can actually fool the calculator with A+Bâˆš2 with many values of A,B even if it doesn't exceed 100.

Edited on May 29, 2015, 12:31 pm
 Posted by Jer on 2015-05-29 12:26:22

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