Question

Thực hiện phép tính: (\(\sqrt{8+2\sqrt{15}}\)-\(\sqrt{7-2\sqrt{10}}\))(\(\sqrt{3}\)-\(\sqrt{2}\))

Answer 1

`(\sqrt{8+2\sqrt{15}}-\sqrt{7-2\sqrt{10}})(\sqrt{3}-\sqrt{2})`

`=(\sqrt{3+2\sqrt{3}.\sqrt{5}+5}-\sqrt{2-2\sqrt{2}.\sqrt{5}+5})(\sqrt{3}-\sqrt{2})`

`=(\sqrt{(\sqrt{3}+\sqrt{5})^2}-\sqrt{(\sqrt{2}-\sqrt{5})^2})(\sqrt{3}-\sqrt{2})`

`=(|\sqrt{3}+\sqrt{5}|-|\sqrt{2}-\sqrt{5}|)(\sqrt{3}-\sqrt{2})`

`=(\sqrt{3}+\sqrt{5}-\sqrt{5}+\sqrt{2})(\sqrt{3}-\sqrt{2})`

`=(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})`

`=3-2=1`