Question

√24 + √27 in the form of k√3

Answer 1

`√(24)+√(27) ~~ \begin{cases} 24=2\cdot 2\cdot 2\cdot 3\\ \qquad 2^2\cdot 2\cdot 3\\ 27=3\cdot 3\cdot 3\\ \qquad 3^2\cdot 3 \end{cases}\implies √(2^2\cdot 2\cdot 3)+√(3^2\cdot 3) \\\\\\ 2√(2\cdot 3)+3√(3)\implies 2√(2)\cdot √(3)+3√(3)\implies \stackrel{\textit{common factoring}}{\underset{ \textit{\LARGE k} }{(2√(2)+3)} ~~ √(3)}`