Bagaimana anda mempermudah (sqrt 3 -sqrt 6) / (sqrt 3 + sqrt6)?

Jawapan:

# = - 3 + 2sqrt (2) #

Penjelasan:

Apabila anda mempunyai jumlah dua akar persegi, silap mata akan didarab dengan penolakan bersamaan:

# (sqrt (3) -sqrt (6)) / (sqrt (3) + sqrt (6)) #

(3) -sqrt (6)) / (sqrt (3) + sqrt (6)) * #

(= ((sqrt (3)) ^ 2-2 * sqrt (3) * sqrt (6) + (sqrt (6)) ^ 2) ^ 2 #

# = (3-2sqrt (18) +6) / (3-6) #

# = (9-2 * sqrt (9 * 2)) / - 3 #

# = (9-2 * 3sqrt (2)) / - 3 #

# = - 3 + 2sqrt (2) #