Answer 1

`T=sqrt{8-2sqrt{15}}/(sqrt{10}-sqrt6)`

`=sqrt{5-2sqrt{5,3}+3}/(sqrt2(sqrt5-sqrt3))`

`=sqrt{(sqrt5-sqrt3)^2}/(sqrt2(sqrt5-sqrt3))`

`=(sqrt5-sqrt3)/(sqrt2(sqrt5-sqrt3))`

`=1/sqrt2`

`=sqrt2/2`

Answer 2

\(T=\dfrac{\sqrt{8-2\sqrt{15}}}{\sqrt{10}-\sqrt{6}}=\dfrac{\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}}{\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)}=\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)}=\dfrac{1}{\sqrt{2}}\)