Square Roots Computed to At Least 10,000 Decimal Places

Enter a number with no more than 10,000 digits:

Accuracy level (maximum decimal places):

100 digits

250 digits

500 digits

1000 digits

2500 digits

5000 digits

10000 digits

20000 digits

40000 digits

60000 digits

80000 digits

100000 digits

120000 digits

The square root of a positive number "x" is defined to be that number "a" that has the property that "a" multiplied by "a" is equal to "x".
Results computed to at most 120,000 decimal places are available here for all positive integers between 1 and 100,000. The results for numbers which are prime were computed at the rate of approximately one every 2 minutes and 23 seconds (per processor) on a home computer in the year 2010 by using the "long division" type approach generally taught in elementary schools years ago.

Results for composite integers through 100,000 were computed by multiplying the square roots of two factors of the composite number which were already computed. This multiplication took about 3 seconds per composite numbers that have no factors that are perfect squares and 1 second for composite numbers which did have a perfect square for a factor.

For non-integers and for numbers greater than 100,000, results are calculated in real time to at most the first 10,000 digits using a "Newton's method" approach.

For those wishing to automate queries to this page, use the following format to return the square root of "x" to 500 decimal places where x equals (for example) 123.456:
http://www.markknowsnothing.com/cgi-bin/sqrroots.php?x=123.456&acc=500
Only one such request will be honored in any two-minute period.