\(C=2\sqrt{37+20\sqrt{3}}-\sqrt{73-40\sqrt{3}}\)
\(=2\sqrt{\sqrt{12^2}+2.5\sqrt{12}+5^2}-\sqrt{\left(4\sqrt{3}\right)^2-2.5.4\sqrt{3}+5^2}\)
\(=2\sqrt{\left(\sqrt{12}+5\right)^2}-\sqrt{\left(4\sqrt{3}-5\right)^2}\)
\(=2.\left|\sqrt{12}+5\right|-\left|4\sqrt{3}-5\right|\)
\(=2.\left(\sqrt{12}+5\right)-\left(4\sqrt{3}-5\right)\)
\(=2\sqrt{12}+10-4\sqrt{3}+5\)
\(=4\sqrt{3}-4\sqrt{3}+10+5\)
\(=15\)
Vậy C = 15
`C=2\sqrt(37+20sqrt3)-sqrt(73-40sqrt3)`
`=2\sqrt((2sqrt3+5)^2)-\sqrt((4sqrt3-5)^2)`
`=2(2sqrt3+5)-(4sqrt3-5)`
`=4sqrt3+10-4sqrt3+5`
`=15`
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Hằng đẳng thức: `A^2+-2AB+B^2=(A+-B)^2`
Khai căn: `sqrt(A^2)=|A|={(A\text(,nếu )A>=0),(-A\text(,nếu )A<0):}`
