Com simplifiqueu sqrt (400/5)?

Resposta:

Mirar abaix.

Explicació:

#sqrt (400/5) = sqrt (400) / sqrt (5) #

#sqrt (400) / sqrt (5) = 20 / sqrt5 #

# = 20 / sqrt (5) * sqrt (5) / sqrt (5) #

# = (20sqrt (5)) / 5 = 4sqrt5 #

Resposta:

#sqrt (400/5) = 4sqrt (5) #

Explicació:

#sqrt (400/5) = sqrt (400) / sqrt (5) = 20 / sqrt (5) #

Volem racionalitzar el denominador. Aquí només estem eliminant l’arrel quadrada, que es mostra en blau.

# 20 / sqrt (5) = (20color (blau) (sqrt (5))) / (sqrt (5) * color (blau) (sqrt (5))) = (20sqrt5) / 5 = 4sqrt (5) #

Què és (sqrt (5+) sqrt (3)) / (sqrt (3+) sqrt (3+) sqrt (5)) - (sqrt (5-) sqrt (3)) / (sqrt (3+) sqrt (3-) sqrt (5))?

2/7 Prenem, 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) - (sqrt5-sqrt3) ) (2sqrt3 + sqrt5)) / ((2sqrt3 + sqrt5) (2sqrt3-sqrt5) = ((2sqrt15-5 + 2 * 3-sqrt15) - (2sqrt15 + 5-2 * 3-sqrt15)) / ((2sqrt3) ^ 2- (sqrt5) ^ 2) = (cancel·lar (2sqrt15) -5 + 2 * 3cancel (-sqrt15) - cancel·lar (2sqrt15) -5 + 2 * 3 + cancel·lar (sqrt15)) / (12-5) = ( -10 + 12) / 7 = 2/7 Tingueu en compte que si en els denomina

Com simplifiqueu (1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) div sqrt (a + 1) / (( (a-1) sqrt (a + 1) - (a + 1) sqrt (a-1)), a> 1?

Formatatge matemàtic enorme ...> color (blau) (((1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) ) / (sqrt (a + 1) / ((a-1) sqrt (a + 1) - (a + 1) sqrt (a-1))) = color (vermell) (((1 / sqrt (a- 1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a-1)))) / (sqrt (a +1) / (sqrt (a-1) cdot sqrt (a-1) cdot sqrt (a + 1) -sqrt (a + 1) cdot sqrt (a + 1) sqrt (a-1))) = color ( blau) (((1 / sqrt (a-1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a -1)))) / (sqrt (a + 1) / (sqrt (a + 1) cdot sqrt (a-1) (sqrt (a-1) -sqrt (a + 1))) = color (vermell) ((1 /

Simplifiqueu l’expressió ?: 1 / (sqrt (144) + sqrt (145)) + 1 / (sqrt (145) + sqrt (146)) + ... + 1 / (sqrt (168) + sqrt (169))

1 Primer nota que: 1 / (sqrt (n + 1) + sqrt (n)) = (sqrt (n + 1) -sqrt (n)) / ((sqrt (n + 1) + sqrt (n)) ( sqrt (n + 1) -sqrt (n)) color (blanc) (1 / (sqrt (n + 1) + sqrt (n))) = (sqrt (n + 1) -sqrt (n)) / ((( n + 1) -n) color (blanc) (1 / (sqrt (n + 1) + sqrt (n)) = sqrt (n + 1) -sqrt (n) So: 1 / (sqrt (144) + sqrt (145)) + 1 / (sqrt (145) + sqrt (146)) + ... + 1 / (sqrt (168) + sqrt (169)) = (sqrt (145) -sqrt (144)) + (sqrt (146) -sqrt (145)) + ... + (sqrt (169) -sqrt (168)) = sqrt (169) -sqrt (144) = 13-12 = 1