Yes, there is a correct way to spell 'congratulations'. In contrast, since 'congradulations' is not a recognised word in the English language, there can arguably be no right, or indeed wrong, way of spelling it because it is essentially a meaningless combination of sounds. The two are completely separate things, one of which is accepted as a proper word in the English language - in that it is both found in respected dictionaries which clarify such things for example, the Oxford English Dictionary, and in that it is in widely used circulation within English speaking countries - the other is not a word in common usage, but could be viewed as a slang word. The word 'congratulations' (con-gra-TU-la-tions) is defined as 'An expression of praise for an achievement or good wishes on a special occasion', it can also be interpreted as 'the act of congratulating'. Thus, in an everyday sentence it could be used in this way: "congratulations on that promotion!" or "our congratulations to today's the prize winner". On the other hand, 'congradulations' would in most cases be seen as a misspelling of congratulations. The only other meaning it seems to have is as a slang term. For example, the commonly used website www.urbandctionary.com, defines 'congradulations' in a variety of ways, such as: "what morons give each other when they graduate community college." as well as "a tongue in cheek misspelling of 'congratulations' that's a play on the word graduate.". Alternatively, it offers suggestions that it could be used as a way of saying 'congratulations' which also gets across the speaker's sarcasm. So although there is only one proper way of spelling 'congratulations', there is also the possibility of making a distinction between that word and the less used, and, as I have explained ,less recognised slang word derived from it, which is spelt as 'congradulations'.
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