Question

rationalise 3√3-1 upon 2√7-1

Answer 1

Hello!

$\dfrac{3\sqrt{3}-1}{2\sqrt{7}-1} \\ \\ \implies \dfrac{3\sqrt{3}-1}{2\sqrt{7}-1} \times \dfrac{2\sqrt{7}+1}{2\sqrt{7}+1} \\ \\ \implies \dfrac{(3\sqrt{3}-1)(2\sqrt{7}+1)}{(2\sqrt{7})^{2} - (1)^{2}} \\ \\ \implies \dfrac{6\sqrt{21}+3\sqrt{3}-2\sqrt{7}-1}{4 \times 7 - 1} \\ \\ \implies \dfrac{6\sqrt{21}+3\sqrt{3}-2\sqrt{7}-1}{28 - 1} \\ \\ \implies \boxed{\red{\bf{\dfrac{6\sqrt{21}+3\sqrt{3}-2\sqrt{7}-1}{27}}}}$

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