Somehow, you made it complicated. It is 31622.776585872405015194191707146...
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999999999
There are infinitely many of them. They include square root of (4.41) square root of (4.42) square root of (4.43) square root of (4.44) square root of (4.45) square root of (5.3) square root of (5.762) square root of (6) square root of (6.1) square root of (6.2)
999999999 times 999993 is 999,992,999,000,007
A principal square root is any square root that's answer is positive, and a perfect square root is a square root that's answer is an integer.
square root of 20 = square root of 4 * square root of 5. square root of 4 = 2, so your answer is 2 square root of 5.