Wat is de vereenvoudigde vorm van vierkantswortel van 10 - vierkantswortel van 5 over vierkantswortel van 10 + vierkantswortel van 5?

Antwoord:

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

Uitleg:

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

#color (wit) ("XXX") = annuleren (sqrt (5)) / uitschakelen (sqrt (5)) * (sqrt (2) -1) / (sqrt (2) 1) #

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

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

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

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