Surds are irrational numbers that can be expressed with a root symbol (√). Simplifying surds means expressing them in their simplest form, where the number under the root sign (the radicand) has no square factors other than 1. For example, $\sqrt{8}$ can be simplified to $2\sqrt{2}$ because 8 has a square factor of 4. Mastering surd simplification is essential for GCSE Maths in the UK, as it allows for easier calculations and comparisons. Understanding perfect squares and prime factorization are key tools.
Match the term to its definition:
| Term | Definition |
|---|---|
| 1. Surd | A. The number under the root symbol |
| 2. Radicand | B. A number that cannot be expressed as a simple fraction |
| 3. Simplify | C. Expressing a surd in its lowest terms |
| 4. Rational Number | D. A number that can be expressed as a fraction p/q |
| 5. Irrational Number | E. A number that cannot be expressed as a fraction p/q |
To simplify $\sqrt{12}$, we first find the largest square factor of 12, which is ____. Then, we can write $\sqrt{12}$ as $\sqrt{4 \times 3}$. This simplifies to ____$\sqrt{3}$. Thus, $\sqrt{12}$ simplified is ____$\sqrt{3}$.
Explain why it's important to simplify surds when solving mathematical problems. Give a practical example where simplifying a surd makes a calculation easier.
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