53. \( \frac{2 \sqrt{6}}{\sqrt{3}} \)

To simplify \( \frac{2 \sqrt{6}}{\sqrt{3}} \), you can first rewrite the expression by separating the square root in the denominator. This leads to: \[ \frac{2 \sqrt{6}}{\sqrt{3}} = 2 \cdot \frac{\sqrt{6}}{\sqrt{3}} = 2 \cdot \sqrt{\frac{6}{3}} = 2 \cdot \sqrt{2} = 2\sqrt{2}. \] So, the simplified form of \( \frac{2 \sqrt{6}}{\sqrt{3}} \) is \( 2\sqrt{2} \). In mathematics, simplifying expressions not only makes them easier to work with but also helps to uncover underlying patterns. Mastering simplification techniques can significantly boost your problem-solving skills and confidence. Additionally, practice really makes perfect! Take a variety of problems and try to simplify them in different ways or using different methods. This can help you identify common mistakes like overlooking square roots or mismanaging radicals, refining your math agility.