One such example is tablet YBC 7289 (that is, Yale Babylonian Collection, no. 7289), a small disk about 8 cm in diameter and 8 mm thick. It shows a square and its diagonals. On one of them (shown horizontally here), the following is written in Babylonian numerals:
In sexagesimal notation (which also applies to fractions), this means:
1+2460+51602+10303=305470216000≈1,414212961 + \dfrac{24}{60} + \dfrac{51}{60^2} + \dfrac{10}{30^3} = \dfrac{305470}{216000} \approx 1,41421296
This is an excellent approximation to 2=1,414213562,\sqrt{2} = 1,414213562,
accurate to five decimal places!
Note that the upper-left side of the square bears the inscription
that is, 30, while beneath the diagonal is written 42 25 35, which is interpreted as
42+2560+35602≈302,42 + \dfrac{25}{60} + \dfrac{35}{60^2} \approx 30\sqrt{2},
which is indeed the length of the diagonal of a square with side length 30.

Tablet YBC 7289 as it appears (left)

and with some of the numbers highlighted (right).