(0) \( \sqrt{255^{3} p^{10}} \) (3) \( 202 \sqrt{323^{3} y^{10}} \) (5) \( \sqrt{2} \times \sqrt{8} \) (6) \( \sqrt[10]{9 x^{10}+16 x^{10}} \) (9) \( \sqrt{3 m^{3}} \times \sqrt{27 m} \) (11) \( \frac{\sqrt{9 x^{0}}-\sqrt{4 x^{10}}}{5 x^{3}} \)

When simplifying expressions involving square roots, it helps to remember that you can break down the numbers under the square root into their prime factors. This can often make it easier to pull out perfect squares, which can greatly simplify your calculations. For example, \( \sqrt{8} \) is \( \sqrt{4 \times 2} \), which simplifies to \( 2\sqrt{2} \). In mathematics, especially algebra, a common mistake is forgetting to account for coefficients or variables when simplifying. For instance, when working with \( \sqrt{a^2} \), many students mistakenly simplify it to just \( a \) without considering if \( a \) could be negative, which leads to losing the negative root. Always keep in mind the absolute value when dealing with square roots!