The first four digits of an eight-digit perfect square are 2012. Find its square root?

2 Answers
Apr 28, 2017

+-2sqrt503

Explanation:

2012=2^2*503
And 503 is a prime number
Because 22^2<503<23^2
So the square root of 2012 is
+-sqrt2012=+-2sqrt503

See below.

Explanation:

We have

sqrt(20120000) approx 4485.53

This square root can be extracted manually

https://en.wikipedia.org/wiki/Methods_of_computing_square_roots

and

4485^2 = 20115225

so the number is

4486->4486^2= 20124196