(2.247)3 + (1.730)3 + (1.023)3 - 3 x 2.247 x 1.730 x 1.023 / ( (2.247)2 + (1.730)2 + (1.023)2 - (2.247 x 1.730) - (1.730 x 1.023) - (2.247 x 1.023) )

We know that, a³ + b³ + c³ - 3abc = (a + b + c ) ( a² + b² + c² - ab - bc - ca )
⇒ (a + b + c) = ( a³ + b³ + c³ - 3abc ) / ( a² + b² + c² - ab - bc - ca ) .......................(i)
Given that in question,
(2.247)³ + (1.730)³ + (1.023)³ - 3 x 2.247 x 1.730 x 1.023 / (2.247)² + (1.730)² + (1.023)² - (2.247 x 1.730) - (1.730 x 1.023) - (2.247 x 1.023)
Apply the formula given in Equation (i) and we will get,
= ( a + b + c )
= ( 2.247 + 1.730 + 1.023) [ from eq. (i) ]
= 5.000 = 5