The smallest squares containing k 22's :
225 = 15²,   2202256 = 1484²,   2212291225 = 47035²,
2222222266944 = 1490712²,   122222200822225 = 11055415².

The first integer which is the sum of 7 squares in just two ways (see 20).

Every integer greater than 22 is the sum of 9 nonzero squares.

22² = 484, 4 + 8 + 4 = 4².

22² = 2! + 2! + 5! + 5! + 5! + 5!.

22² = 484 is a palindromic square.

22² = 2³ + 2³ + 5³ + 7³.

22² = 484, every digit of which is even. There are only 3-digits squares consisting of even digits.

22⁸ = 54875873536, 5 + 48 + 7 + 58 + 7 + 353 + 6 = 22²,
22¹⁰ = 26559922791424, 2² + 6² + 5² + 59² + 9² + 2² + 2² + 79² + 14² + 24² = 22³,
22¹¹ = 584318301411328, 5 + 8 + 4 + 3 + 1 + 8 + 3 + 01 + 411 + 32 + 8 = 22² and more 43 equations,

(22² + 2) = (4² + 2)(5² + 2) = (1² + 2)(2² + 2)(5² + 2),
(22² - 4) = (3² - 4)(10² - 4),   (22² + 6)= (1² + 6)(8² + 6),
(22² - 8) = (5² - 8)(6² - 8).

22² + 23² + 24² + ... + 6910² = 331668²,
22² + 23² + 24² + ... + 80² = 413².

(1² + 2² + 3² + 4²)(5² + 6² + ... + 12²)(13²)(14² + 15² + ... + 22²) = 96720².

Komachi Fractions : (3/22)² = 1539/82764 = 7695/413820, (22/31)² = 13068/25947, (22/89)² = 4356/71289.

Komachi Square Sum : 22² = 2² + 3² + 4² + 6² + 7² + 8² + 9² + 15².

Komachi: 22² = 12 * 34 - 5 - 6 + 78 + 9 and more 31 equations.
Komachi: 22² = 98 - 7 * 6 - 5 + 432 + 1 and more 35 equations.
Komachi: 22² = 1² + 2² * 3² * 4² - 5² - 6² - 7² - 8² + 9².
Komachi: 22² = 9² - 8² - 7² - 6² - 5² + 4² * 3² * 2² + 1².

1² + 2² + 3² + ... + 22² = 3795, which consists of different odd digits.

1³ + 2³ + 3³ + 4³ + ... + 22³ = (1 + 2 + 3 + 4 + ... + 22)² = 253².

22² = 484 appears in the decimal expressions of π and e:
  π = 3.14159•••484••• (from the 2363rd digit),
  e = 2.71828•••484••• (from the 781st digit).