Shows way to divide irrational denominators (14)

I believe the answer is:

demonstrations

'shows' is the definition.
(demonstration is a kind of show)

'way to divide irrational denominators' is the wordplay.
'way' becomes 'st'.
'to divide' indicates putting letters inside.
'irrational' indicates anagramming the letters.
'denominators' is an anagram of 'demonrations'.
'st' going within 'demonrations' is 'DEMONSTRATIONS'.

(Another definition for demonstrations that I've seen is " protests".)

I've seen this clue in The Independent.

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