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I really don't see the point of calculating a square root with such a precision. The 10 or 12 significant digits provided by most scientific calculators (or the 15-16 significant digits provided by Excel) are more than enough for most purposes. If you need random digits, there are better ways to do that.

In any case, at Wolfram Alpha you can get lots of digits for a square root. In this case, you can use the input "root 11", and then repeatedly click on "more digits". I don't know whether it goes up to 10,000 digits, though - especially without a paid subscription. I'll leave it to you to find that out.

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Q: What Is The Square Root The Number 11 To 10000 Digits?
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How many numbers does the square root have?

The number of digits in the square root of a number depends on the number. If it is a square number, the square root will have a finite number of digits. If the number is not a square number then the square root will be an irrational number with an infinite, non-repeating decimal representation. In both cases, the number of digits before the decimal point, in the square root of x will be the rounded value of 1+0.5*log10(x)


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