What is the square root of 123423?

Let’s assume, just for laughs, that you are in the middle of the woods with no Internet-capable device or calculator in sight. You only have a log table. You must find the square root of  123423, or that fierce tiger will eat you whole. I am going to teach you to get rid of this situation.

 Here, I am using the logarithmic relation to find the square root of the number 123423.

  • I am using the relation

log ((x)^1/2)=1/2 log x

  • Now replace the value of “x” with “123423”.

log ((123423)^1/2) = 1/2 (log 123423)

=1/2(log 0.123423 *10^6)

=1/2(6+log 0.123423)

From the logbook, log 0.123423=-0.90863

so log ((123423)^1/2)=2.54685

Therefore (123423)^1/2= 10^2.54685 = 352.202491

Which is nearly equal to the actual value 351.316097, yeah?

You are safe now. 😉