Estimating the Square Root of a Number Less Than 1
The method below is for decimal numbers less than one. If you have a
No problem was given in
fraction, change the fraction to a decimal and use the procedure given
below. There are methods for calculating the square root of a fraction,
but they are not covered in this subcourse.
(1) Pair off the digits of the number beginning at the decimal point
and going to the right.
(2) Identify the first digit pair with a non-zero digit.
(a) The identified pair must contain two digits, not just one.
(b) If the first non-zero is at the end of the number and there is
an odd number of digits to the right of the decimal, then
you must add a zero to the end of the number to make the
last digit part of a pair of digits.
(c) Drop all digits (if any) following this digit pair.
(3) Replace the remaining pairs of digits.
(a) If the pair identified in step 2 is a perfect square
(1, 4, 9, 16, 25, 36, 49, 64, or 81), replace the pair with the
square root of that number.
(b) If the pair identified in step 2 is not a perfect square,
identify the largest perfect square that is less than the pair
and replace the pair with the square root of that perfect
(c) For each pair of double zero digits between the decimal
point and the digit pair identified in step 2, substitute a
(4) The resulting number is the estimated square root (low).
(5) Increase the last digit of the estimated square root (low) by 1
to arrive at the estimated square root (high).
(6) The actual square root will be less than the estimated square
root (high) and equal to or greater than the estimated square
NOTE: If the pair of digits identified in step 2 is a perfect square and
there were no non-zero digits following the pair in the original number,
then the estimated square root (low) is the actual square root.
Estimate the square root of the following numbers.
b. 0. 0004645775