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.


square root of ab = square root of a x square root of b

square root of a x square root of a = a


√2 × √6 = √12 (= 2× 6)

= √4 × √3

= 2√3

Addition and Subtraction

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)


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




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