Question

simplify
sqrt 5- sqrt 10
------------
sqrt 5+sqrt 10

Answer 1

sqrt 5- sqrt 10 (sqrt 5-sqrt 10)*(sqrt 5-sqrt 10) (sqrt 5-sqrt 10)^2
---------------=--------------------------------=-------------------
(sqrt 5+sqrt 10) (sqrt 5+sqrt 10)*(sqrt 5-sqrt 10) 5-10

(sqrt 5-sqrt 10)^2
=-----------------
-5

Answer 2

\[(\sqrt{5}-\sqrt{10})/(\sqrt{5}+\sqrt{10})\]
\[(\sqrt{5}-\sqrt{10})*(\sqrt{5}-\sqrt{10})\div(\sqrt{5}+\sqrt{10})(\sqrt{5}-\sqrt{10})\]
\[5+10-2*(\sqrt{5}*\sqrt{10}) \]
---------------------
(5-10)