>> syms a

>> eq=7*a+1/(7*a) == sqrt(98)

eq =

7*a + 1/(7*a) == 7*2^(1/2)

>> sa=solve(eq,a)

sa =

2^(1/2)/2 - 94^(1/2)/14

2^(1/2)/2 + 94^(1/2)/14

>> eval(sa(1))

ans =

        0.0145810872699291

>> eval(sa(2))

ans =

          1.39963247510317

>> sa(1)^777

ans =

(2^(1/2)/2 - 94^(1/2)/14)^777

>> eval(ans)

ans =

     0

>> sa(2)^777

ans =

(2^(1/2)/2 + 94^(1/2)/14)^777

>> eval(ans)

ans =

     2.83717616726445e+113

     

saying a =  sqrt(2)/2 -/+ sqrt(94)/14

Apparently, when the minus sign is used, the 777th power is zero (but don't count on it exactly--see below), but when the plus sign is used, the 777th power is approximately 2.837... x 10^113.

Wolfram Alpha formulates a different form:

a = 7 +/- sqrt(47))/(7 sqrt(2)

but they evaluate to the same approximations.

However, the 777th power of the smaller value is not zero but approximately

1.83975297887821163258528183970279248931825398362582135131... × 10^-1427

and the 777th power of the larger value is approximately

2.8371761672641754912015188779177168044380334845625931196230... × 10^113.