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Verified answer
12^1/2 - 24^3/2= √12 - √24^3
= √4 . √3 - √24² . √24
= 2√3 - 24√24
= 2√3 - 24(√4 × √6)
= 2√3 - 24 . 2√6
= 2√3 - 48√6
= (2√3)(1 - 24√2)