¿Cómo simplificar sqrt (9x ^ 2) / sqrt (18y ^ 2)?

Responder:

# x / (sqrt (2) y) #

Explicación:

#sqrt (9x ^ 2) / sqrt (18y ^ 2) #

# sqrt9 = 3 #

#sqrt (x ^ 2) = x #

# sqrt18 = sqrt (9xx2) = 3sqrt2 #

#sqrt (y ^ 2) = y #

Por lo tanto

#sqrt (9x ^ 2) / sqrt (18y ^ 2) = (3x) / (3sqrt (2) y) #=# x / (sqrt (2) y) #

¿Cómo simplificar (sqrt (2) * sqrt (2)) + (sqrt (2) * -sqrt (2)) + (0 * 0)?

= 0 (sqrt2 * sqrt2) + (sqrt2 * -sqrt2) + (0 * 0) = (sqrt4) + (- sqrt4) + (0) = (2) + (- 2) + (0) = 2 - 2 + 0 = 0

¿Cómo simplificar (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?

Formato de matemáticas enorme ...> color (azul) (((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 (rojo) (((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 ( azul) ((((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 (rojo) ((1 / sqr

¿Simplificar la expresión ?: 1 / (sqrt (144) + sqrt (145)) + 1 / (sqrt (145) + sqrt (146)) + ... + 1 / (sqrt (168) + sqrt (169))

1 Primero note que: 1 / (sqrt (n + 1) + sqrt (n)) = (sqrt (n + 1) -sqrt (n)) / ((sqrt (n + 1) + sqrt (n)) ( sqrt (n + 1) -sqrt (n)) color (blanco) (1 / (sqrt (n + 1) + sqrt (n))) = (sqrt (n + 1) -sqrt (n)) / (( n + 1) -n) color (blanco) (1 / (sqrt (n + 1) + sqrt (n)) = sqrt (n + 1) -sqrt (n) Por lo tanto: 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