Sub-topic 1
2024 · National Preliminary
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Simplifying $\dfrac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}$ and $\dfrac{\sqrt{11}-\sqrt{7}}{\sqrt{11}+\sqrt{7}}$
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Sub-topic 2
2025 · National Preliminary
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Rationalising $\dfrac{11(4+\sqrt{5})}{4-\sqrt{5}}$ and $\dfrac{7(5+3\sqrt{2})}{5-3\sqrt{2}}$
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Sub-topic 3
2025 · National Preliminary
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Simplifying $\dfrac{5+2\sqrt{5}}{5-2\sqrt{5}}$
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Sub-topic 4
2013 · National Preliminary
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Simplifying $\dfrac{3\sqrt{2}-4\sqrt{5}}{\sqrt{10}}$
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Sub-topic 5
2013 · National Preliminary
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Multiplying the conjugates $(4+3\sqrt{5})(4-3\sqrt{5})$
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Sub-topic 6
2013 · National Preliminary
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Simplifying $(\sqrt{1500}+2\sqrt{15})(\sqrt{15}-3)$
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Sub-topic 7
2019 · National Preliminary
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Rationalising $\dfrac{3}{\sqrt{5}-\sqrt{2}}$
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Sub-topic 8
2021 · National Quarterfinal
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Expanding $(1+\sqrt{3})^3$
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Sub-topic 9
2026 · National Preliminary
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Rationalising $\dfrac{5-2\sqrt{3}}{5+2\sqrt{3}}$
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Sub-topic 10
2024 · National One-Eighth
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Solving $\sqrt{2x^2-9}=x$, $\sqrt{5x^2-36}=2x$ and $\sqrt{\dfrac{3x^2}{2}-2}=x$
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Sub-topic 11
2022 · National Final
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Solving $\left(\sqrt[3]{2x-4}\right)^2=4$
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