평방근 125 + 제곱근 1/5 - 제곱근 49/5를 어떻게 단순화합니까?

평방근 125 + 제곱근 1/5 - 제곱근 49/5를 어떻게 단순화합니까?
Anonim

대답:

# sqrt125 + sqrt (1/5) -sqrt (49/5) = 19 / sqrt5 #

설명:

# sqrt125 = sqrt (25 * 5) = sqrt (25 * 25 / 5) = sqrt (25 ^ 2 / 5) = sqrt (25 ^ 2) / sqrt5 = 25 / sqrt5 #

#sqrt (1/5) = sqrt1 / sqrt5 = 1 / sqrt5 #

#sqrt (49/5) = sqrt (7 ^ 2 / 5) = sqrt (7 ^ 2) / sqrt5 = 7 / sqrt5 #

#rarr sqrt125 + sqrt (1/5) -sqrt (49/5) = 25 / sqrt5 + 1 / sqrt5-7 / sqrt5 = (25 + 1-7) / sqrt5 = 19 / sqrt5 #