8+2√7 3+√7
√(----------------) - √( ---------------- ) * √2 =
8-2√7 3-√7
избавимся от иррациональности в знаменателе
(8+2√7)*(8+2√7 ) (3+√7)*(3+√7)
√(----------------------------- ) - √( ----------------------- ) * √2 =
(8-2√7)*(8+2√7 ) (3-√7)*(3+√7)
---------------------------------------------------------------------------------------------
(8+2√7)² ( 3+√7)²
√(------------------- ) - √( ----------------- ) * √2 =
8²-(2√7)² (3²-√7²)
---------------------------------------------------------------------------------------------
(8+2√7)² ( 3+√7)²
√(------------------- ) - √( ----------------- ) * √2 =
64- 28 9 --7
------------------------------------------------------------------------------------------
(8+2√7)² ( 3+√7)²
√(------------------- ) - √( ----------------- ) * √2 =
36 2
-------------------------------------------------------------------------------------------
8+2√7 3+√7
------------------- - ( ----------------- ) * √2 =
6 √ 2
---------------------------------------------------------------------------------------------
2(4+√7) 4+√7 4+√7 -9-3√7
----------------- - ( 3+√7) = ------------ - ( 3+√7) = ---------------------- =
6 3 3
------------------------------------------------------------------------------------------
-5-2√7
= ---------------
3