Surds and simplifying them
Split the number under a root into factors and take each pair out: β12 = 2β3. Multiply roots, add like surds, and rationalise a denominator.
π Start here: read the steps of the βLessonβ in order (1, 2, 3 β¦) and answer each question. Then continue with βPracticeβ.
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Guide
This studio follows GCSE N8 (Higher): simplifying surds, adding and multiplying them, and rationalising denominators.
β12 is the square root of 12: the number that, multiplied by itself, makes 12. It is not a whole number, so we keep it exact as a surd.
β(2Γ2Γ3): a pair of equal factors under the root comes out as one, because β(2Γ2) = 2. So β12 = 2β3.
On the board, tap a root, then Split: the number under it is written as primes. Tap two equal chips under the root to take the pair out. Tap one root and then another to join them into one root.
Type your answer on the keypad. The β key writes a root over the number after it: 2, β, 3 gives 2β3.