Simplify the number into simplest radical form. Use the Select a composite number to break into factors. Continue factor tree to help determine the factors. factoring until all factors are prime. \( \sqrt{96} \) \( \sqrt{6} \) \( 2 \sqrt{6} \) \( 4 \sqrt{6} \) \( 4 \sqrt{3} \)

To simplify \( \sqrt{96} \), we start by breaking down the number into factors. The prime factorization of 96 is \( 2^5 \times 3^1 \). Using a factor tree, we can break it down as follows: \( 96 \) splits to \( 48 \times 2 \), \( 48 \) splits to \( 24 \times 2 \), \( 24 \) to \( 12 \times 2 \), \( 12 \) to \( 6 \times 2 \), and \( 6 \) to \( 3 \times 2 \). The prime factors are \( 2, 2, 2, 2, 2, \) and \( 3 \). Now we can simplify \( \sqrt{96} \) using these prime factors. Since there are five \( 2's \), we can take out pairs. This gives us: \[ \sqrt{96} = \sqrt{(2^4) \cdot 2 \cdot 3} = \sqrt{16} \cdot \sqrt{6} = 4\sqrt{6}. \] Thus, the simplest radical form of \( \sqrt{96} \) is \( 4\sqrt{6} \). To avoid any common missteps in simplification, remember to always look for pairs of prime factors. A common mistake is to skip grouping factors or neglecting to take the square roots of perfect squares, leading to incomplete simplification. Always strive to simplify to the lowest radical form for clarity!