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Key Concepts
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1. Definition
A surd is an irrational root of a rational number (e.g., √2, ∛5). If ⁿ√a is irrational, it is a surd.
2. Rationalizing the Denominator
The process of removing a radical from the denominator of a fraction.
- For 1/√a, multiply numerator and denominator by √a.
- For 1/(a + √b), multiply by the conjugate (a - √b).
3. Operations with Surds
- √a · √b = √(ab)
- √a / √b = √(a/b)
- a√x ± b√x = (a ± b)√x