
English: 
that is a very interesting application
of the quadratic formula estimating the
square root of a number by dividing two
other numbers the solutions of the
quadratic equation X square minus 6x
minus 1 equals 0 can be approximated
because the quadratic equation is
equivalent to x equals 6 plus 1 X this
has solutions given by the infinite
continued fraction we can easily show
that the sequence of numbers 6 plus 1
over 6 comma 6 plus 1 over 6 plus 1 over
6 8 etc keeps better and better
approximations to one of the solutions
of the quadratic equation the
interesting part is that we can use this
approach to calculate the square root of
40 let me explain we can approximate the

Spanish: 
Raiz cuadradas como fracciones
Podemos usar la formula cuadratica
para aproximar la raiz cuadrada de un numero.
Las soluciones de esta ecuacion,
se pueden aproximar
de la manera siguiente.
La ecuacion equivale a x igual a 6 mas el reciproco de x.
La solucion es el limite de la secuencia que generamos
hallando el reciproco de 6 y sumandole.
El primer termino, el segundo, el tercero, etc
se van aproximando mas y mas a la solucion!
De manera que podemos usar esto para
aproximar la raiz cuadrada de 40.
Veamos como.

English: 
positive solution using the
approximation written as a fraction stop
the video here and see whether you can
write that calculation as a fraction
right 6 plus 1 over 6 is 37 over 6 we
turn the fraction upside down so the
reciprocal is 6 over 37 we had 6 the
reciprocal is 37 over 220 8 plus 6 the
reciprocal is 228 over 1405 finally we
add 6 again 6 times one thousand four
hundred and five plus 228 is a thousand
658 we can approximate the positive

Spanish: 
La solucion positiva
se puede aproximar usando, por ejemplo,  el cuarto termino.
Para el video y simplifica esta fraccion como una sola!
 
Veamos...
6 por 1,405 mas 228 la convierte en unica fraccion.

Spanish: 
Podemos aproximar la solucion como 8,658 entre 1,405
Multiplicando por 2 y restando 6,
aproximamos la raiz cuadrada de 40
dividiendo 8,886 entre 1,405.
 
 
 
 
 

English: 
solution dividing 8650 8 by 1405
multiplying by two and subtracting six
we end up with the fraction a thousand
886 over 1400
and five the square root of 40 can be
approximated dividing those numbers if
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