Verified Answer :

Soham

First, we find the value of 'x.'
  \(x^{3}=729 \\ x= \sqrt[3]{729}\)
x=9

\(x^{2} + \sqrt{x}\)
\(9^{2}\)+\(\sqrt{9}\)
81+3
= 84
\(x^{2} + \sqrt{x}\)=84

Lilith

\(x^3 = 729 \\ \\ x^2+\sqrt{x} =? \\ \\ x^3 - 729=0 \\ \\ x^3-9^3 = 0\\ \\(x-9)(x^2+9x+81)=0\)

\(x^2+9x+81 =0 \ \ or \ \ x-9 = 0\\ \\\Delta =b^2-4ac =9^2-4\cdot 1\cdot 81=81- 324 =-243 \\ \\ and \ we \ know \ when \ \Delta \ is \ negative, \ theres \ no \ solution \\ or \\ x-9=0 \\ \\x=9\)


\(a^3-b^3=(a-b)(a^2+ab+b^2) \\\\ \\ x^2+\sqrt{x} = 9^2+\sqrt{9}=81+3 = 84\)

 

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