Hour of Math · SS3 · Unit SSNP12

Rationalising with Conjugates

Clear a two-term surd denominator by multiplying numerator and denominator by the denominator's conjugate, so the bottom becomes a difference of squares $(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y}) = x - y$. FOIL the numerator, simplify, and express the answer in a required named form such as $x + y\sqrt{2}$ or $p\sqrt{5} + q\sqrt{3}$, watching signs.

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