Question

50 simplify \\(sqrt3{-54}\\)

Explanation:

Step1: Factor -54

We know that \(-54 = -1\times54\), and \(54 = 27\times2=3^{3}\times2\). So \(-54=-1\times3^{3}\times2\).

Step2: Simplify the cube root

Using the property of cube roots \(\sqrt[3]{ab}=\sqrt[3]{a}\times\sqrt[3]{b}\) (for real numbers \(a,b\)) and \(\sqrt[3]{-1}=-1\), \(\sqrt[3]{3^{3}} = 3\).
So \(\sqrt[3]{-54}=\sqrt[3]{-1\times3^{3}\times2}=\sqrt[3]{-1}\times\sqrt[3]{3^{3}}\times\sqrt[3]{2}=- 1\times3\times\sqrt[3]{2}=-3\sqrt[3]{2}\)

Answer:

\(-3\sqrt[3]{2}\)