Question

Simplify root 54 + 5 root 243 -3 root 75

Answer 1

Dear Student,

$$\begin{gathered} \sqrt{54}+5\sqrt{243}-3\sqrt{75} \\ \Rightarrow \sqrt{2\times 3\times 3\times 3}+5\sqrt{3\times 3\times 3\times 3\times 3}-3\sqrt{3\times 5\times 5} \\ \Rightarrow 3\sqrt{6}+45\sqrt{3}-15\sqrt{3} \\ \Rightarrow 3\sqrt{6}+30\sqrt{3} \\ \Rightarrow 3\sqrt{3}\left(\sqrt{2}+10\right) \end{gathered}$$

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