Rationalising The Denominator
Bayani Gaba-gaba
Surds are precise, but a square root lurking in a denominator makes an expression harder to read, harder to compare and harder to simplify. Rationalising the denominator is the technique that removes every irrational part from the bottom of a fraction, leaving a clean rational number underneath.
You will learn two core moves: multiplying by the surd itself when the denominator is a single term, and multiplying by the conjugate when it contains two terms. Both rest on one elegant algebraic fact: the product of conjugate surds is always rational. Master these and you will handle every rationalisation question Edexcel can set.
Manufura
- Rationalise the denominator of expressions involving surds
Takardar Darasi
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- What is the conjugate of 3 + sqrt(5)? A) 3 + sqrt(5) B) 3 - sqrt(5) C) -3 + sqrt(5) D) -3 - sqrt(5) Answer: B
- Rationalise 1 / sqrt(2). Which is correct? A) sqrt(2) B) sqrt(2) / 4 C) sqrt(2) / 2 D) 2 / sqrt(2) Answer: C
- Which identity makes the conjugate method work? A) (a + b)^2 = a^2 + 2ab + b^2 B) (a + b)(a - b) = a^2 - b^2 C) a^2 + b^2 = (a + b)^2 D) (a - b)^2 = a^2 - 2ab + b^2 Answer: B
- What is 8 / (2 * sqrt(2)) in its simplest rationalised form? A) 2 * sqrt(2) B) 4 * sqrt(2) C) sqrt(2) D) 4 / sqrt(2) Answer: A
- Rationalise 1 / (sqrt(6) - sqrt(5)). The denominator becomes: A) 1 B) 11 C) sqrt(30) D) 6 - 5 Answer: A
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