Correct option is (a) 1000
P = 999, then
\(\sqrt[3]{P(P^2 + 3P + 3) + 1}\)
\(= \sqrt[3]{999((999)^2 + 3(999) + 3) + 1}\)
\(= \sqrt[3]{(999)^3 + 3(999)^2 + 3+(999)+ 1}\)
\(= \sqrt[3]{(999+ 1)^3}\)
\(= \sqrt[3]{(1000)^3}\)
\(= {(1000^3)^\frac 13}\)
\(=1000\)