[latex] sqrt 96/ sqrt sqrt 686* sqrt 126[/latex]

[latex] frac{ sqrt{96} }{ sqrt{ sqrt{686*126} } } = frac{ sqrt{96}}{ sqrt{ sqrt{86436} } } = frac{ sqrt{96}}{ sqrt{294} } = sqrt{ frac{4*4*2*3}{3*2*7*7} }= frac{4}{7} [/latex]

V 686 = V ( 7 * 49  * 2 ) = 7 V 7 * 2 V 126 = V ( 2 * 9 * 7 ) = 3 V 7 * 2 V 96 = V ( 2 * 6 * 8 ) =  4 V 6 ------------------------V 686 * V 126 = 21 * 7 * 2 = 294 ------------------------- V 294 =  V 6 *49 = 7 V 6 ----------------------------( 4 V 6 ) : (7 V 6 ) = 4/7 ------------------------------  ответ 4/7