What is easiest way to get the square root of 1,002,001 by hand?

Answer 1

Well 1000 * 1000 = 1 000 000

(1000 + x)(1000 + x) = 1002001

1000000 + 2000x + x^2 = 1002001

x^2 + 2000x = 2001

x^2 + 2000x - 2001 = 0

( x + 2001 )(x - 1 ) = 0

x=1 x = -2001

So the square roots are

1000 + 1 = 1001 and -2001 + 1000 = -1001