Nice Square Root Math Simplification. How to solve

[@SYAN23SYAN13]

Tanks for watching

[@ManojkantSamal]

^= read as to the power
*=read as square root
Let a=11, b=100,
So,
a+b=114
As per the question
*[{(a^4+b^4+(a+b)^4}/2]
Let's explain N
N=a^4+b^4+(a+b)^4
=a^4+b^4+a^4+b^4+{6a^2b^2)+(4a^3b)+(4ab^3)
=2a^4+2b^4+(6^2b^2)+(4a^3b)+(4ab^3)
=2[a^4+b^4+(3a^2b^2)+(2a^3b)+(2ab^3)]
=2[{a^4+b^4+(2a^2b^2)}+{a^2b^2+2ab(a^2+b^2)]
=2[{(a^2)^2+(b^2)^2+(2×a^2.b^2)}+{a^b^2+2ab(a^2+b^2)}]
=2[(a^2+b^2)^2+(ab)^2+2ab(a^2+b^2)]
=2{a^2+b^2+ab}^2
N/D=[2{a^2+b^2+ab}^2]/2
={a^2+b^2+ab}^2
As per question
*[{a^2+b^2+ab}^2]
={a^2+b^2+ab}
Put the values of a, b & c
{(11^2)+(100^2)+(11×100)
=121+10000+1100
=11221

[@z-ryk]

V( (11^4 + 100^4 + 111^4) / 2)
= V( (121² + 10_000² + 12321²) / 2)
= V( (14_641 + 100_000_000 + 151_807_041) / 2)
= V( 251 821 682 / 2)
= V(125 910 841)
= 11 221
J'ai tout posé et pour la racine carrée :
1 25 91 08 41 11221
0 25 1x1 = 1
4 91 21x1 = 1
47 08 222x2 = 444
2 24 41 2242x2 = 4484
22441x1 = 22441