let met try, for [a, b, c], and [d, e, f]

1. Take the log of all terms (allowed, because log keeps the sum monotonic):

log(sqrt(a)) + log(sqrt(b)) + log(sqrt(c))

2. pull out the sqrt from the log:

1/2 * log(a) + 1/2 * log(b) +1/2 * log(c)

3. factor out the 1/2:

1/2 * (log(a) + log(b) + log(c))

4. sum of logs can be rewritten as a log of product:

1/2 * log (a * b * c)

5. compute log of (a * b * c), and halve it. Ditto with log of (d * e * f). This should give a number which is proportional to the original sum of sqrt.