3) \( \sqrt{675}-\sqrt{432}+\sqrt{234} \)

To simplify \( \sqrt{675} - \sqrt{432} + \sqrt{234} \), we need to break each square root down into its prime factors. First, let's simplify \( \sqrt{675} \): \[ 675 = 25 \times 27 = 5^2 \times 3^3 \] Thus, \[ \sqrt{675} = \sqrt{25 \times 27} = \sqrt{25} \times \sqrt{27} = 5 \times 3\sqrt{3} = 15\sqrt{3} \] Next, for \( \sqrt{432} \): \[ 432 = 144 \times 3 = 12^2 \times 3 \] So, \[ \sqrt{432} = \sqrt{144 \times 3} = \sqrt{144} \times \sqrt{3} = 12\sqrt{3} \] Now, simplifying \( \sqrt{234} \): \[ 234 = 9 \times 26 = 3^2 \times 26 \] Therefore, \[ \sqrt{234} = \sqrt{9 \times 26} = \sqrt{9} \times \sqrt{26} = 3\sqrt{26} \] Now we can substitute these results back into the original equation: \[ \sqrt{675} - \sqrt{432} + \sqrt{234} = 15\sqrt{3} - 12\sqrt{3} + 3\sqrt{26} \] Combining like terms gives: \[ (15 - 12)\sqrt{3} + 3\sqrt{26} = 3\sqrt{3} + 3\sqrt{26} \] Factoring out the 3, we find: \[ 3(\sqrt{3} + \sqrt{26}) \] Thus, the final simplified expression is: \[ \boxed{3(\sqrt{3} + \sqrt{26})} \]