sute the rules for surds

Here are the key rules for surds: 1. **Definition**: A surd is an irrational number in radical form, like \( \sqrt{2} \) or \( \sqrt[3]{5} \). 2. **Simplification**: Break down the number under the radical into perfect squares or cubes, e.g., \( \sqrt{50} = 5\sqrt{2} \). 3. **Multiplication**: Multiply surds by multiplying the numbers inside the radicals, e.g., \( \sqrt{a} \times \sqrt{b} = \sqrt{ab} \). 4. **Division**: Divide surds by dividing the numbers inside the radicals, e.g., \( \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \). 5. **Addition/Subtraction**: Only add or subtract like surds (same radicand), e.g., \( a\sqrt{c} + b\sqrt{c} = (a+b)\sqrt{c} \). 6. **Rationalising the Denominator**: Multiply numerator and denominator by a suitable surd to eliminate the radical in the denominator, e.g., \( \frac{1}{\sqrt{a}} = \frac{\sqrt{a}}{a} \). 7. **Higher-Order Roots**: Express roots as exponents, e.g., \( \sqrt[n]{a^m} = a^{\frac{m}{n}} \). These rules help simplify and manipulate surds effectively in mathematical problems.