rút gọn căn(8+căn8+căn 20+căn 40)

`\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}`

`=\sqrt{8 +\sqrt{2.4}+\sqrt{5.4}+\sqrt{10.4}}`

`=\sqrt{8+2\sqrt{2}+2\sqrt{5}+2\sqrt{10}}`

`=\sqrt{1+2+5 +2.1.\sqrt{2} +2.1.\sqrt{5}+2.\sqrt{2}.\sqrt{5}}`

`=\sqrt{(\sqrt{1})^2 +(\sqrt{2})^2 + (\sqrt{5})^2  +2.1.\sqrt{2} +2.1.\sqrt{5}+2.\sqrt{2}.\sqrt{5}}`

`=\sqrt{(\sqrt{1} +\sqrt{2}+\sqrt{5})^2}`

`=\sqrt{1}+\sqrt{2}+\sqrt{5}`

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Áp dụng hằng đẳng thức nâng cao:

`(A+B+C)^2 = A^2 +B^2 +C^2 +2AB +2BC+ 2CA`