Hvordan forenkler du kvadratroden 125 + kvadratroden 1/5 - kvadratroden 49/5?

Hvordan forenkler du kvadratroden 125 + kvadratroden 1/5 - kvadratroden 49/5?
Anonim

Svar:

# Sqrt125 + sqrt (1/5) -sqrt (49/5) = 19 / sqrt5 #

Forklaring:

# 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 #