Svar:
# 7sqrt (3) - 2sqrt (2) #
Forklaring:
#sqrt (3) + sqrt (72) - sqrt (128) + sqrt (108) #
Vi vet det #108 = 9 * 12 = 3^3 * 2^2#, så #sqrt (108) = sqrt (3 ^ 3 * 2 ^ 2) = 6sqrt (3) #
#sqrt (3) + sqrt (72) - sqrt (128) + 6sqrt (3) #
Vi vet det #72 = 9*8 = 3^2*2^3#, så #sqrt (72) = sqrt (3 ^ 2 * 2 ^ 3) = 6sqrt (2) #
#sqrt (3) + 6sqrt (2) - sqrt (128) + 6sqrt (3) #
Vi vet det #128 = 2^7#, så #sqrt (128) = sqrt (2 ^ 6 * 2) = 8sqrt (2) #
#sqrt (3) + 6sqrt (2) - 8sqrt (2) + 6sqrt (3) #
forenkling
# 7sqrt (3) - 2sqrt (2) #
