Câu hỏi của Trần Thị Trà Giang

Question

Thực hiện phép tính:

a)$\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}$

b)$\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}$

c)$\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}$

d)\(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sq...

Mới vô · Accepted Answer

a,

$\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\
=\sqrt{3-2\sqrt{3}+1}+\sqrt{3+2\sqrt{3}+1}\
=\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+1\right)^2}\
=\left|\sqrt{3}-1\right|+\left|\sqrt{3}+1\right|\
=\sqrt{3}-1+\sqrt{3}+1\
=2\sqrt{3}$

b,

$\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\ =\sqrt{24+4\cdot\sqrt{4}\cdot\sqrt{5}}+\sqrt{9-4\sqrt{5}}\ =\sqrt{24+4\sqrt{20}}+\sqrt{9-4\sqrt{5}}\ =\sqrt{20+4\sqrt{20}+4}+\sqrt{5-4\sqrt{5}+4}\ =\sqrt{\left(\sqrt{20}+4\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}\ =\left|\sqrt{20}+4\right|+\left|\sqrt{5}-2\right|\ =\sqrt{20}+4+\sqrt{5}-2\ =2+2\sqrt{5}+\sqrt{5}\ =2+3\sqrt{5}$

c,

$\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\ =\sqrt{17-6\cdot\sqrt{4}\cdot\sqrt{2}}+\sqrt{9+2\cdot\sqrt{4}\cdot\sqrt{2}}\
=\sqrt{17-6\sqrt{8}}+\sqrt{9+2\sqrt{8}}\
=\sqrt{9-6\sqrt{8}+8}+\sqrt{8+2\sqrt{8}+1}\
=\sqrt{\left(3-\sqrt{8}\right)^2}+\sqrt{\left(\sqrt{8}+1\right)^2}\
=\left|3-\sqrt{8}\right|+\left|\sqrt{8}+1\right|\
=3-\sqrt{8}+\sqrt{8}+1\
=4$

d,

$\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\
=\sqrt{6-4\sqrt{2}}+\sqrt{22-4\cdot\sqrt{9}\cdot\sqrt{2}}\
=\sqrt{6-4\sqrt{2}}+\sqrt{22-4\sqrt{18}}\
=\sqrt{4-4\sqrt{2}+2}+\sqrt{18-4\sqrt{18}+4}\
=\sqrt{\left(2-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{18}-2\right)^2}\
=\left|2-\sqrt{2}\right|+\left|\sqrt{18}-2\right|\
=2-\sqrt{2}+\sqrt{18}-2\
=-\sqrt{2}+\sqrt{18}\
=-\sqrt{2}+3\sqrt{2}\
=2\sqrt{2}$Câu trả lời: a,

$\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\
=\sqrt{3-2\sqrt{3}+1}+\sqrt{3+2\sqrt{3}+1}\
=\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+1\right)^2}\
=\left|\sqrt{3}-1\right|+\left|\sqrt{3}+1\right|\
=\sqrt{3}-1+\sqrt{3}+1\
=2\sqrt{3}$

b,

$\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\ =\sqrt{24+4\cdot\sqrt{4}\cdot\sqrt{5}}+\sqrt{9-4\sqrt{5}}\ =\sqrt{24+4\sqrt{20}}+\sqrt{9-4\sqrt{5}}\ =\sqrt{20+4\sqrt{20}+4}+\sqrt{5-4\sqrt{5}+4}\ =\sqrt{\left(\sqrt{20}+4\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}\ =\left|\sqrt{20}+4\right|+\left|\sqrt{5}-2\right|\ =\sqrt{20}+4+\sqrt{5}-2\ =2+2\sqrt{5}+\sqrt{5}\ =2+3\sqrt{5}$

c,

$\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\ =\sqrt{17-6\cdot\sqrt{4}\cdot\sqrt{2}}+\sqrt{9+2\cdot\sqrt{4}\cdot\sqrt{2}}\
=\sqrt{17-6\sqrt{8}}+\sqrt{9+2\sqrt{8}}\
=\sqrt{9-6\sqrt{8}+8}+\sqrt{8+2\sqrt{8}+1}\
=\sqrt{\left(3-\sqrt{8}\right)^2}+\sqrt{\left(\sqrt{8}+1\right)^2}\
=\left|3-\sqrt{8}\right|+\left|\sqrt{8}+1\right|\
=3-\sqrt{8}+\sqrt{8}+1\
=4$

d,

$\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\
=\sqrt{6-4\sqrt{2}}+\sqrt{22-4\cdot\sqrt{9}\cdot\sqrt{2}}\
=\sqrt{6-4\sqrt{2}}+\sqrt{22-4\sqrt{18}}\
=\sqrt{4-4\sqrt{2}+2}+\sqrt{18-4\sqrt{18}+4}\
=\sqrt{\left(2-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{18}-2\right)^2}\
=\left|2-\sqrt{2}\right|+\left|\sqrt{18}-2\right|\
=2-\sqrt{2}+\sqrt{18}-2\
=-\sqrt{2}+\sqrt{18}\
=-\sqrt{2}+3\sqrt{2}\
=2\sqrt{2}$

Mới vô · Answer

b,

$\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\
=\sqrt{24+4\cdot\sqrt{4}\cdot\sqrt{5}}+\sqrt{9-4\sqrt{5}}\
=\sqrt{24+4\sqrt{20}}+\sqrt{9-4\sqrt{5}}\
=\sqrt{20+4\sqrt{20}+4}+\sqrt{5-4\sqrt{5}+4}\
=\sqrt{\left(\sqrt{20}+2\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}\
=\left|\sqrt{20}+2\right|+\left|\sqrt{5}-2\right|\
=\sqrt{20}+2+\sqrt{5}-2\
=\sqrt{20}+\sqrt{5}\
=\sqrt{4}\cdot\sqrt{5}+\sqrt{5}\
=2\sqrt{5}+\sqrt{5}\
=3\sqrt{5}
$Câu trả lời: b,

$\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\
=\sqrt{24+4\cdot\sqrt{4}\cdot\sqrt{5}}+\sqrt{9-4\sqrt{5}}\
=\sqrt{24+4\sqrt{20}}+\sqrt{9-4\sqrt{5}}\
=\sqrt{20+4\sqrt{20}+4}+\sqrt{5-4\sqrt{5}+4}\
=\sqrt{\left(\sqrt{20}+2\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}\
=\left|\sqrt{20}+2\right|+\left|\sqrt{5}-2\right|\
=\sqrt{20}+2+\sqrt{5}-2\
=\sqrt{20}+\sqrt{5}\
=\sqrt{4}\cdot\sqrt{5}+\sqrt{5}\
=2\sqrt{5}+\sqrt{5}\
=3\sqrt{5}
$

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