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### Surd Calculations?

Surds are numbers left in 'square root form' (or 'cube root form' etc). They are therefore irrational numbers. Surds are the root of numbers and not whole numbers.

Multiplication

Example:

√2 × √6 = √12 (= 2× 6)

= √4 × √3

= 2√3

4√3 - 2√3 = 2√3

5√5 + 8√5 = 13√5

Note: 5√7 + 3√3 cannot be manipulated because the surds are different (one is √7 and one is √3)

Example:

Simplify √12 + √27

12 = 3 × 4. So √12 = √(3 × 4) = √3 × √4 = 2 × √3.

Similarly, √27 = 3√3.

Hence √12 + √27 = 2√3 + 3√3 = 5√3

2 years ago

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