Rút gọn biểu thức ($\sqrt[]{6}$ + $\sqrt[]{2}$)($\sqrt[]{3}$ – 2)$\sqrt[]{\sqrt[]{3}+ 2}$ 15/08/2021 Bởi Camila Rút gọn biểu thức ($\sqrt[]{6}$ + $\sqrt[]{2}$)($\sqrt[]{3}$ – 2)$\sqrt[]{\sqrt[]{3}+ 2}$
$(\sqrt{6} + \sqrt{2})(\sqrt{3} – 2)\sqrt{\sqrt{3} + 2}$ $= \sqrt{2}(\sqrt{3} + 1)(\sqrt{3} – 2)\sqrt{\sqrt{3} + 2}$ $(\sqrt{3} + 1)(\sqrt{3} – 2)\sqrt{2(\sqrt{3} + 2)}$ $= (\sqrt{3} + 1)(\sqrt{3} – 2)\sqrt{4 + 2\sqrt{3}}$ $= (\sqrt{3} + 1)(\sqrt{3} – 2)\sqrt{(\sqrt{3} + 1)^2}$ $= (\sqrt{3} + 1)(\sqrt{3} – 2)(\sqrt{3} + 1)$ $= (3 + 1 + 2\sqrt{3})(\sqrt{3} – 2)$ $= (4 + 2\sqrt{3})(\sqrt{3} – 2)$ $= 2(\sqrt{3} + 2)(\sqrt{3} – 2) = 2(3 – 4) = 2. (- 1) = – 2$ Bình luận
$(\sqrt{6} + \sqrt{2})(\sqrt{3} – 2)\sqrt{\sqrt{3} + 2}$
$= \sqrt{2}(\sqrt{3} + 1)(\sqrt{3} – 2)\sqrt{\sqrt{3} + 2}$
$(\sqrt{3} + 1)(\sqrt{3} – 2)\sqrt{2(\sqrt{3} + 2)}$
$= (\sqrt{3} + 1)(\sqrt{3} – 2)\sqrt{4 + 2\sqrt{3}}$
$= (\sqrt{3} + 1)(\sqrt{3} – 2)\sqrt{(\sqrt{3} + 1)^2}$
$= (\sqrt{3} + 1)(\sqrt{3} – 2)(\sqrt{3} + 1)$
$= (3 + 1 + 2\sqrt{3})(\sqrt{3} – 2)$
$= (4 + 2\sqrt{3})(\sqrt{3} – 2)$
$= 2(\sqrt{3} + 2)(\sqrt{3} – 2) = 2(3 – 4) = 2. (- 1) = – 2$
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