# Square root of 2

The square root of 2 is very important number in mathematics. However it is generally overshadowed by other interesting quantities like PI. While PI is the circumference of a unit circle, the square root of 2 is the diagonal of a unit square.

The square root of 2 is, of course, related to PI as that sqrt(2)=2sin(PI/4). Fortunately, it is much easier to compute the numeric value of the square root of 2 than it is to compute PI.

It is also of some historical interest since it was the first known irrational number. The proof of the irrationality of the square root of 2 is actually quite elegant.

The first 1000 digits or so of the square root of 2 that I have calculated are shown below: =

• 1.

4142135623 7309504880 1688724209 6980785696 7187537694 8073176679 7379907324 7846210703 8850387534 3276415727 3501384623 0912297024 9248360558 5073721264 4121497099 9358314132 2266592750 5592755799 9505011527 8206057147 0109559971 6059702745 3459686201 4728517418 6408891986 0955232923 0484308714 3214508397 6260362799 5251407989 6872533965 4633180882 9640620615 2583523950 5474575028 7759961729 8355752203 3753185701 1354374603 4084988471 6038689997 0699004815 0305440277 9031645424 7823068492 9369186215 8057846311 1596668713 0130156185 6898723723 5288509264 8612494977 1542183342 0428568606 0146824720 7714358548 7415565706 9677653720 2264854470 1585880162 0758474922 6572260020 8558446652 1458398893 9443709265 9180031138 8246468157 0826301005 9485870400 3186480342 1948972782 9064104507 2636881313 7398552561 1732204024 5091227700 2269411275 7362728049 5738108967 5040183698 6836845072 5799364729 0607629969 4138047565 4823728997 1803268024 7442062926 9124859052 1810044598 4215059112 0249441341 7285314781 0580360337 1077309182 8693147101 7111168391 6581726889 4197587165 8215212822 9518488472 08969

• This took about 15 mins. to compute on my 486-33. It was calulated by applying Newton's Method to the curve y=x*x, and solving of x when y=2. 5,000,000 Digits of the sqrt(2) computed by NASA

These guys have better computers than I have.

Source Code

High precision C++ integer math library:

Square root of 2 demonstration (requires above library):

High precision C++ floating point math library:

(Requires above integer math library)

Compute your own square root to 70 or 300 places!!! Note: 300 places might take a few seconds

Precision: 70 Places 300 Places

Number to take square root of?