62 (number)

62 (sixty-two) is the natural number following 61 and preceding 63.

62 is: As a consequence of the mathematical coincidence that 106 − 2 = 999,998 = 62 × 1272, the decimal representation of the square root of 62 has a curiosity in its digits:[5]

62

{\displaystyle {\sqrt {62}}}

= 7.874 007874 011811 019685 034448 812007 … For the first 22 significant figures, each six-digit block is 7,874 or a half-integer multiple of it.

7,874 × 1.5 = 11,811 7,874 × 2.5 = 19,685 The pattern follows from the following polynomial series:

{\displaystyle {\begin{aligned}(1-2x)^{-{\frac {1}{2}}}&=1+x+{\frac {3}{2}}x^{2}+{\frac {5}{2}}x^{3}+{\frac {35}{8}}x^{4}+{\frac {63}{8}}x^{5}+\cdots \end{aligned}}}

Plugging in x = 10−6 yields