Number · Surds
Chapter 1 · 4
The idea
Expanding brackets with surds
Why surds multiply out exactly like algebra — with √a·√a collapsing to a — how squares like (4 − √2)² keep their middle term, and why conjugate pairs multiply to a whole number.
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Number · Surds
Expanding brackets with surds
Why surds multiply out exactly like algebra — with √a·√a collapsing to a — how squares like (4 − √2)² keep their middle term, and why conjugate pairs multiply to a whole number.
Why it works
Treat √3 like x — with one collapse
Brackets with surds expand by exactly the rules you already know from algebra — treat the way you'd treat . The only new move is that collapses to , so surd expansions simplify after expanding in a way algebra can't.Single brackets
. Multiply through, collapse any , collect. When multiplying mixed terms, coefficients multiply with coefficients and roots with roots: .Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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