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Simplify the following radicals.

1. \(\sqrt{832}\)
   
   
   Solution

   \(\begin{align}
    \sqrt{832} &= \sqrt{64\cdot 13}  \\
     &= \sqrt{64} \cdot \sqrt{13}  \\
     &= 8\sqrt{13}  \\
    \end{align}\)
   
   
   
   
2. \(\sqrt[{3}]{1\thinspace 600}\)
   
   
   Solution

   \(\begin{align}
    \sqrt[3]{{1\thinspace 600}} &= \sqrt[3]{{64\cdot 25}} \\
     &= \sqrt[3]{{64}}\cdot \sqrt[3]{{25}} \\
     &= 4\sqrt[3]{{25}} \\
    \end{align}\)
   
   
   
   
3. \(\sqrt[3]{{27r^4s^2}}\)
   
   
   Solution

   \(\begin{align}
    \sqrt[3]{{27r^4s^2}} &= \sqrt[3]{{27r^3rs^2}} \\
     &= \sqrt[3]{{27}}\cdot \sqrt[3]{{r^3}}\cdot \sqrt[3]{{rs^2}} \\
     &= 3r\sqrt[3]{{rs^2}} \\
    \end{align}\)