Question

\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{20}+3}}\) tính ghi rõ các bước

Answer 1

\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{20}+3}}\\ =\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\\ =\sqrt{\sqrt{5}-\sqrt{5-2\sqrt{5}+1}}\\ =\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}}\\ =\sqrt{\sqrt{5}-\left(\sqrt{5}-1\right)}\\ =\sqrt{\sqrt{5}-\sqrt{5}+1}\\ =\sqrt{1}=1\)

Answer 2

`\sqrt{\sqrt{5}-\sqrt{3-\sqrt{20}+3}}`

`=\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}`

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

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

`=\sqrt{\sqrt{5}-|\sqrt{5}-1|}`

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

`=\sqrt{1}`

`=1`