(a) Write $\sqrt{108}$ in the form $k \sqrt{3}$

Step 1 ：Write \(\sqrt{108}\) in the form \(k \sqrt{3}\)

Step 2 ：The first step is to simplify the square root of 108. We can do this by finding the prime factorization of 108 and then simplifying the square root.

Step 3 ：The prime factorization of 108 is \(2^2 * 3^3\).

Step 4 ：We can then simplify the square root by taking out pairs of prime factors. In this case, we can take out a pair of 2s and a pair of 3s, leaving us with \(2 * 3 * \sqrt{3}\), or \(6\sqrt{3}\).

Step 5 ：Final Answer: \(\sqrt{108}\) in the form \(k \sqrt{3}\) is \(\boxed{6\sqrt{3}}\).