Câu hỏi của Lizy

Question

tính$\sqrt{28-10\sqrt{3}}$$\sqrt{41+12\sqrt{5}}$$\sqrt{32-10\sqrt{7}}$$\sqrt{11-4\sqrt{7}}$

乇尺尺のﾚ · Accepted Answer

$\sqrt{28-10\sqrt{3}}\
=\sqrt{3-10\sqrt{3}+25}\
=\sqrt{\left(\sqrt{3}-5\right)^2}\
=\left|\sqrt{3}-5\right|\
=5-\sqrt{3}$$\sqrt{41+12\sqrt{5}}\
=\sqrt{5+12\sqrt{5}+36}\
=\sqrt{\left(\sqrt{5}+6\right)}\
=\left|\sqrt{5}+6\right|\
=\sqrt{5}+6$$\sqrt{32-10\sqrt{7}}\
=\sqrt{7-10\sqrt{7}+25}\
=\sqrt{\left(\sqrt{7}-5\right)^2}\
=\left|\sqrt{7}-5\right|\
=5-\sqrt{7}$$\sqrt{11-4\sqrt{7}}\
=\sqrt{7-4\sqrt{7}+4}\
=\sqrt{\left(\sqrt{7}-2\right)^2}=\left|\sqrt{7}-2\right|\
=\sqrt{7}-2$Câu trả lời: $\sqrt{28-10\sqrt{3}}\
=\sqrt{3-10\sqrt{3}+25}\
=\sqrt{\left(\sqrt{3}-5\right)^2}\
=\left|\sqrt{3}-5\right|\
=5-\sqrt{3}$$\sqrt{41+12\sqrt{5}}\
=\sqrt{5+12\sqrt{5}+36}\
=\sqrt{\left(\sqrt{5}+6\right)}\
=\left|\sqrt{5}+6\right|\
=\sqrt{5}+6$$\sqrt{32-10\sqrt{7}}\
=\sqrt{7-10\sqrt{7}+25}\
=\sqrt{\left(\sqrt{7}-5\right)^2}\
=\left|\sqrt{7}-5\right|\
=5-\sqrt{7}$$\sqrt{11-4\sqrt{7}}\
=\sqrt{7-4\sqrt{7}+4}\
=\sqrt{\left(\sqrt{7}-2\right)^2}=\left|\sqrt{7}-2\right|\
=\sqrt{7}-2$

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