一些二次根试计算(1)(根号下8a^3/c^4)/(-根号下ab/2c^2)(2)3(根号下2)/(根号下5)-2(3)3-根号下2/3+根号下2(4)X^2-2y/X+根号下2Y

Question

一些二次根试计算
(1)(根号下8a^3/c^4)/(-根号下ab/2c^2)
(2)3(根号下2)/(根号下5)-2
(3)3-根号下2/3+根号下2
(4)X^2-2y/X+根号下2Y

Answer 1

(1)(根号下8a^3/c^4)/(-根号下ab/2c^2)
=-根号下((8a^3/c^4)/(ab/2c^2))
=-根号下(16a^2/bc^2)
=-根号下(16a^2*b/(bc)^2)
=-4a*(根号下b)/b|c|
(2)3(根号下2)/[(根号下5)-2]
= {3(根号下2)*[(根号下5)+2]}/{[(根号下5)-2]*[(根号下5)-2]}
=3(根号下2)*[(根号下5)+2]/[5-4]
=3(根号下2)*[(根号下5)+2]
=3(根号下10)+6根号下2
(3)(3-根号下2)/(3+根号下2)
=[(3-根号下2)*(3-根号下2)]/[(3+根号下2)(3-根号下2)]
= (3-根号下2)^2/[9-2]
=[9+2-6根号下2]/7
=11/7-6根号下2/7
(4)(X^2-2y)/(X+根号下2Y)
=[(X^2-2y)*(X-根号下2Y)]/[(X+根号下2Y)*(X-根号下2Y)]
=[(X^2-2y)*(X-根号下2Y)]/[X^2-2y]
=X-根号下2Y)