Shachar Brown asked:

In the Gemara, Rav Acha says a man is permitted to carry an object in 'Reshut Harabim' up to the length of a diagonal of of a 4 'Amot' square. Rashi explains this would come out 5.6 (4 & 8/5) Amot. I personally calculated the square on a calculator and came to- 28.28 instead of 28 tefachim(!!!!!) a whole thumb wrong!! How could rashi mislead us? He was always so precise!

Shachar Brown, Jerusalem, Israel

The Kollel replies:

Shachar, that is an excellent question. Actually, Rashi was simply relying on the Gemara in a number of places in Shas which measures the diagonal of a square as 1.4 times its side (see Eruvin 57a) instead of 1.414 times its side, as your calculator figures it. In this particular case, measuring the diagonal in the Gemara's manner will be "Lo Dak l'Chumra," which is acceptable (Sukah 8a). However, there certainly are times where calculating the diagonal in this manner will bring us a Kula.

Tosfos (Sukah 8a DH Kol) asks your question and does not provide an answer. He asks a similar question on the Rabbinic reckoning of Pi as 3 (instead of 3.14159) in Eruvin 14a DH veha'Ika. Please have a look at our Insights to the Daf (in the book or online) to Eruvin 14:2, as it answers your question as well. In brief, the Rabanan found sources in the Torah to rely on an approximation of these irrational numbers and not to round them off to more than a single decimal point.

So it is true that Rashi's figure is not exact, but we are allowed to be non-exacting in such cases according to the Halachah.

Best wishes,

Mordecai Kornfeld