`G=\sqrt{3+\sqrt{5}}+\sqrt{7-3\sqrt{5}}-\sqrt{2}`
`\sqrt{2}G=\sqrt{2}.(\sqrt{3+\sqrt{5}}+\sqrt{7-3\sqrt{5}}-\sqrt{2})`
`\sqrt{2}G=\sqrt{6+2\sqrt{5}}+\sqrt{14-6\sqrt{5}}-\sqrt{4}`
`\sqrt{2}G=\sqrt{\sqrt{5}^2+2\sqrt{5}+1}+\sqrt{3^3-6\sqrt{5}+\sqrt{5}^2}-2`
`\sqrt{2}G=\sqrt{(\sqrt{5}+1)^2}+\sqrt{(3-\sqrt{5})^2}-2`
`\sqrt{2}G=\sqrt{5}+1+3-\sqrt{5}-2`
`\sqrt{2}G=2`
`G=\sqrt{2}`
