Pencil-and-Paper Math

Getting the square root of a number without the aid of a calculator

by castillo_et

For Three Digits and Beyond

Example:

Get the square root of 2012:

Procedure:

(1) Consider the first two digits of the given value.

20

(2) Figure out two consecutive numbers that when squared will be the closest values to the

considered value of (1).

4 ; 42 = 16

20

5 ; 52 = 25

(3) Add necessary ZEROs. When the resulting values of (2) plus the added zeros are squared, they

must be neither too less nor too much to the given value.

40 ; 402 = 1600

2012

50 ; 502 = 2500

(For this example, one zero each is enough.)

(4) If the given value is midway between the two squared resulting values of (3), get the mean of the

two to arrive for a much closer amount. Otherwise select the closer one between the two.

Checking:

452 = 2025

2025 is closest to 2012 considering 1600 and 2500

(5) Divide the given value by the resulting value of (4).

(6) If the given value is not a perfect square value, state the answer, at least, in two decimal places.

= 44.71

(7) Add the quotient and the denominator and divide it by two.

(8) The answer would be the estimated required value.

Manual computation Using a calculator

44.855

44.85532298

Very close! Not Bad.

Next: Solution using Differential Calculus.