How to solve 3√(20 + 14√2), the cube root, not 3 * bla bla bla?

Question

I know the answer = 2 + √2

but it didn't work out when i tried to calculate it
i did it by equating coefficents

20 + 14√2 = (d + e √2)^3
I expanded the brackets and equate coefficients with and without √2, and got these 2 equations

d^3 + 6de^2 = 20
2e^3 + 3ed^2 = 14

and I am having major difficulty in solving them
the equations are correct, by substituting d = 2 and e = 1

So the problem is, how to solve these 2 equations, i tried the substitution method and it got up to a polynomial of d or e to the power of 9, which is a cubic equation of (d or e) cube, and i know it can be solved by the way of solving cubic equations, but this seems to be too much of a trouble for an answer of 1 and 2, so, the question is...... does anyone have a better insight in solving those equations

Help us out please! Thank you very much!

Answer 1

(d+sqrt(e))^3=d^3+3ed+(e+3d^2)sqrt(e)

Hence
d^3+3ed=20
e+3d^2=14

inside the root is 2
therefore e=2

3d^2=14-2=12
d^2=4
d=2

hence
the answer is 2+sqrt(2)

Answer 2

i dont know but thanks for the points and i would recommend that you use a calculator to work that one out, it looks like it might take a few seconds to work it out, i could do it in my head but i wouldnt want to show off in front of you

Answer 3

You solve it be repeatedly posting the question on here, until someone posts the correct reply!

10 points please?