Please solve the square root of 3998 with a mathematical log table?

Question

i have a little problem with it. DO NOT USE A CALCULATOR

Answer 1

Taking the log of (3998)^(1/2) gives

log [ (3998)^(1/2) ]

(1/2) log [ 3998 ]

(1/2) log(3.998 * 10^3)

(1/2) [ log(3.998) + log(10^3) ]

(1/2) [ log(3.998) + 3 ]

Looking up log(4) on log table, I get 0.6020600.  So adding 3 and dividing by 2 gives 1.80103.  But this is the log of the answer.

10^(1.80103) = 10^1 * 10^0.80103.  Do some extrapolation and you should get about 63.229.