log根号2（根号（6+4根号2）－根号（6-4根号2))=logsqrt(2)(sqrt((2+sqrt(2))^2)-sqrt((2-sqrt(2))^2))=logsqrt(2)((2+sqrt(2))-(2-sqrt(2)))=logsqrt(2)(2sqrt(2))=logsqrt(2)((sqrt(2))^3)=3

Question

log根号2（根号（6+4根号2）－根号（6-4根号2))
= log_sqrt(2)(sqrt((2+sqrt(2))^2) - sqrt((2-sqrt(2))^2))= log_sqrt(2)((2+sqrt(2))-(2-sqrt(2)))= log_sqrt(2)(2sqrt(2))= log_sqrt(2)((sqrt(2))^3)= 3

Answer 1

根号（6+4根号2）=根号（2+根号2）的平方=2+根号2
根号（6-4根号2）=根号（2-根号2）的平方=2-根号2
所以
log根号2（根号（6+4根号2）－根号（6-4根号2))
=log根号2（2+根号2－2+根号2)
=log根号2（2根号2）
=log根号2（根号2）的立方
=3