Kaj je (2sqrt (7) + 3sqrt (2)) (sqrt (7) - 5sqrt (2))?

Odgovor:

# - (16 + 7sqrt14) #

Pojasnilo:

# (2 * sqrt (7) + 3 * sqrt (2)) * (sqrt (7) - 5 * sqrt (2)) #

# = 2sqrt7 ^ 2-10sqrt7 * sqrt2 + 3sqrt2 * sqrt7-15sqrt2 ^ 2 #

# = 2 * 7-7sqrt2 * sqrt7-15 * 2 #

# = 14-30-7sqrt (2 * 7) #

# = - 16-7sqrt14 #

ali:

# = - (16 + 7sqrt14) #

Kako poenostavite (3sqrt (18)) / sqrt (48) - (2sqrt (6)) / sqrt (80)?

(9sqrt2) / (4sqrt3) - (2sqrt6) / (4sqrt5) V redu, to je lahko napačno, ker sem se na kratko dotaknil te teme, toda to je tisto, kar bi naredil: (3sqrt (9xx2)) / sqrt (16xx3) - (2sqrt6) ) / sqrt (16xx5) Kateri je enak (9sqrt2) / (4sqrt3) - (2sqrt6) / (4sqrt5) Upam, da je to prav, prepričan sem, da me bo nekdo popravil, če se motim.

Kaj je 2sqrt {32} + 3sqrt {50} - 3sqrt {18}?

14sqrt (2) barva (modra) (32 = 4 ^ 2 * 2 rarr sqrt (32) = 4sqrt (2)) barva (rdeča) (50 = 5 ^ 2 * 2 rarr sqrt (50) = 5sqrt (2)) barva (zelena) (18 = 3 ^ 2 * 2 rarr sqrt (18) = 3sqrt (2)) Zato barva (bela) ("XXX") 2barva (modra) (sqrt (32)) + 3 barva (rdeča) (sqrt) (50)) - barva (zelena) (sqrt (18)) barva (bela) ("XXX") = 2 * barva (modra) (4sqrt (2)) + 3 * barva (rdeča) (5sqrt (2)) -3 * barva (zelena) (3sqrt (2)) barva (bela) ("XXX") = 8sqrt (2) + 15sqrt (2) -9sqrt (2) barva (bela) ("XXX") = 14sqrt (2 )

Kaj je (sqrt (5+) sqrt (3)) / (sqrt (3+) sqrt (3+) sqrt (5)) - (sqrt (5-) sqrt (3)) / (sqrt (3+) sqrt (3-) sqrt (5))?

2/7 vzamemo, A = (sqrt5 + sqrt3) / (sqrt3 + sqrt3 + sqrt5) - (sqrt5-sqrt3) / (sqrt3 + sqrt3-sqrt5) = (sqrt5 + sqrt3) / (2sqrt3 + sqrt5) - (sqrt5) -sqrt3) / (2sqrt3-sqrt5) = (sqrt5-sqrt3) / (2sqrt3-sqrt5) = ((sqrt5 + sqrt3) (2sqrt3-sqrt5) - (sqrt5-sqrt3) ) (2sqrt3 + sqrt5) ((2sqrt15-5 + 2 * 3-sqrt15) - (2sqrt15-5 + 2 * 3-sqrt15)) / ((2sqrt3)) ^ 2- (sqrt5) ^ 2) = (prekliči (2sqrt15) -5 + 2 * 3zaključi (-sqrt15) - prekliči (2sqrt15) -5 + 2 * 3 + prekliči (sqrt15)) / (12-5) = ( -10 + 12) / 7 = 2/7 Upoštevajte, da če je v imenovalcu (sqrt3 + sqrt (3 + sqrt5)) in (sqrt3 + sqrt (3-sqrt5)), bo odgovor spremenjen.