`(\sqrt{100^2 +100^2 }-(\sqrt{2}+\sqrt{3}))^2`

`=(\sqrt{10000+10000}-(\sqrt{2}+\sqrt{3}))^2`

`=(\sqrt{20000}-(\sqrt{2}+\sqrt{3}))^2`

`=(100\sqrt{2}-\sqrt{2}-\sqrt{3})^2`

`=(99\sqrt{2}-\sqrt{3})^2`

`=(99\sqrt{2})^2 -2.99\sqrt{2}.\sqrt{3}+(\sqrt{3})^2`

`=9801.2 -198\sqrt{6}+3`

`=19605 -198\sqrt{6}`