Câu hỏi của Mỹ Hạnh

Question

A)$\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)$

B)$\left(\sqrt{2}+1^{ }\right)^3-\left(\sqrt{2}-1\right)^3$ C)\(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\s...

qwerty · Accepted Answer

a) $\sqrt{2-\sqrt{3}}\left(\sqrt{6}+\sqrt{2}\right)$

$=\sqrt{2-\sqrt{3}}\sqrt{\left(\sqrt{6}+\sqrt{2}\right)^2}$

$=\sqrt{\left(2-\sqrt{3}\right)\left(\sqrt{6}+\sqrt{2}\right)^2}$

$=\sqrt{\left(2-\sqrt{3}\right)\left(6+2\sqrt{12}+2\right)}$

$=\sqrt{\left(2-\sqrt{3}\right)\left(6+4\sqrt{3}+2\right)}$

$=\sqrt{\left(2-\sqrt{3}\right)\left(8+4\sqrt{3}\right)}$

$=\sqrt{\left(2-\sqrt{3}\right)\cdot4\left(2+\sqrt{3}\right)}$

$=\sqrt{\left(4-3\right)\cdot4}$

$=\sqrt{1\cdot4}$

$=\sqrt{4}$

$=2$

b) $\left(\sqrt{2}+1\right)^3-\left(\sqrt{2}-1\right)^3$

$=2\sqrt{2}+6+3\sqrt{2}+1-\left(2\sqrt{2}-6+3\sqrt{2}-1\right)$

$=2\sqrt{2}+6+3\sqrt{2}+1-\left(5\sqrt{2}-7\right)$

$=2\sqrt{2}+6+3\sqrt{2}+1-5\sqrt{2}+7$

$=0+14$

$=14$

c) $\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}$

dài quá ==' cả d, e, f nữa ==' có j rảnh lm cho nhé :DCâu trả lời: a) $\sqrt{2-\sqrt{3}}\left(\sqrt{6}+\sqrt{2}\right)$