Multiplying Surds Flashcards

GCSE Mathematics (Edexcel) 1MA1

Surd

An irrational number that cannot be simplified to remove a square root (or cube root, etc.).

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Terms in this set (10)

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Surd

An irrational number that cannot be simplified to remove a square root (or cube root, etc.).

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Simplifying a surd

Expressing a surd in its simplest form by factoring out square numbers.

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Rule for multiplying surds

√a × √b = √(a × b)

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Example: √2 × √3

√2 × √3 = √6

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Simplifying √12

√12 = √(4 × 3) = √4 × √3 = 2√3

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Multiplying a simplified surd

Multiply the numbers outside the surds and the numbers inside the surds separately.

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Example: 2√3 × 3√2

2√3 × 3√2 = (2 × 3)(√3 × √2) = 6√6

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Rationalising the denominator

The process of removing a surd from the denominator of a fraction.

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Example: Rationalise 1/√2

Multiply numerator and denominator by √2: (1/√2) × (√2/√2) = √2/2

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Key property of surds

Surds follow the same rules of arithmetic as other numbers, but you cannot add or subtract unlike surds.

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