Number · Surds
Chapter 1 · 3
The idea
Rationalising the denominator
Why multiplying top and bottom by the same thing changes nothing, how √a in a denominator is cleared by √a, and how a conjugate clears a two-term denominator like 3 + √5.
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Number · Surds
Rationalising the denominator
Why multiplying top and bottom by the same thing changes nothing, how √a in a denominator is cleared by √a, and how a conjugate clears a two-term denominator like 3 + √5.
Why it works
Multiply by a clever form of 1
"Rationalise the denominator" means: rewrite the fraction so no surd is left underneath. The tool is the most innocent fact in fractions: multiplying top and bottom by the same number multiplies the fraction by — the value doesn't change, only its appearance. (Multiplying only the bottom is not allowed: that genuinely changes the number.) The entire topic is choosing which form of makes the surd downstairs disappear.Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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