Wie multiplizieren und vereinfachen Sie # frac {5 sqrt {3} * 3 sqrt {15}} {4 sqrt {5} * 2 sqrt {75}} #?

Antworten:

# (5sqrt (3) * 3sqrt (15)) / (4sqrt (5) * 2sqrt (75)) = (9sqrt (5)) / (8sqrt (15) #

Erläuterung:

# (5sqrt (3) * 3sqrt (15)) / (4sqrt (5) * 2sqrt (75)) #

# = (5 * 3sqrt (15 ** 3)) / (4 * 2sqrt (75 ** 5) #

# = (5 * 3sqrt (5 * 3 * 3)) / (4 * 2sqrt (5 * 5 * 3 * 5) #

# = (15 * sqrt (5 * 3 ^ 2)) / (8 * sqrt (5 * 5 * 3 * 5) #

# = (15 * 3 * sqrt (5)) / (8 * sqrt (5 * 3 * 5 ^ 2) #

# = (15 * 3 * sqrt (5)) / (8 * 5 * sqrt (5 * 3) #

# = (45 * sqrt (5)) / (40 * sqrt (15) #

# = (9 * sqrt (5)) / (8 * sqrt (15) #