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Natural number
62 (sixty-two) is the natural number following 61 and preceding 63.
62 as the sum of three distinct positive squares.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:
( 1 − 2 x ) − 1 2 = 1 + x + 3 2 x 2 + 5 2 x 3 + 35 8 x 4 + 63 8 x 5 + ⋯ {\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 1 999 , 998 {\displaystyle {\frac {1}{\sqrt {999,998}}}} , and 62 {\displaystyle {\sqrt {62}}} = 7 , 874 × 1 999 , 998 {\displaystyle {7,874}\times {\frac {1}{\sqrt {999,998}}}} .
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