b) \( \sqrt{\frac{4^{2} \times 9^{2}}{2^{2} \times 3^{2}}} \)

To simplify the expression \( \sqrt{\frac{4^{2} \times 9^{2}}{2^{2} \times 3^{2}}} \), we can start by rewriting the squares: 1. Calculate \( 4^2 \) and \( 9^2 \) to get \( 16 \) and \( 81 \) respectively. 2. Calculate \( 2^2 \) and \( 3^2 \) to get \( 4 \) and \( 9 \) respectively. Now, plug these values back into the expression: \[ \sqrt{\frac{16 \times 81}{4 \times 9}} \] Now simplifying the numerator and denominator: - The numerator: \( 16 \times 81 = 1296 \) - The denominator: \( 4 \times 9 = 36 \) So, we have: \[ \sqrt{\frac{1296}{36}} = \sqrt{36} = 6 \] Thus, the simplified form of the expression is \( 6 \).