Apakah bentuk akar kuadrat yang disederhanakan dari 10 - akar kuadrat dari 5 di atas kuadrat dari 10 + akar kuadrat dari 5?

Menjawab:

# (sqrt (10) -sqrt (5)) / (sqrt (10) + sqrt (5) = 3-2sqrt (2) #

Penjelasan:

# (sqrt (10) -sqrt (5)) / (sqrt (10) + sqrt (5) #

#color (white) ("XXX") = cancel (sqrt (5)) / cancel (sqrt (5)) * (sqrt (2) -1) / (sqrt (2) +1) #

#color (white) ("XXX") = (sqrt (2) -1) / (sqrt (2) +1) * (sqrt (2) -1) / (sqrt (2) -1) #

#color (white) ("XXX") = (sqrt (2) -1) ^ 2 / ((sqrt (2) ^ 2-1 ^ 2) #

#color (white) ("XXX") = (2-2sqrt2 + 1) / (2-1) #

#color (white) ("XXX") = 3-2sqrt (2) #