Divide: (sqrt(2) - 7) / (sqrt(2) + 4)

15/7 - (11/14) sqrt(2)

-15/7 - (11/14) sqrt(2)

13/7 + (11/14) sqrt(2)

-15/7 + (11/14) sqrt(2)

47/14

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb