What is the value of the folowing?

Question

What is the value of:
(7 + sqrt(50))^(1/3) + (7 - sqrt(50))^(1/3)
[ Do not use calculator ]

Answer 1

2

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I use here v instead of sqrt for better visibility:
7 + v50=7+5v2=1+3v2+6+2v2=(1+v2)^3 --->(1)
7 - v50=7-5v2=1-3v2+6-2v2=(1-v2)^3 ---> (2)
Using above equations in given one we get :
(1) ^(1/3)=1+v2
(2) ^(1/3)=1-v2
1+v2+1-v2=2