 So, Lyohue presents a method of finding square roots, but what if our radicand isn't a perfect square? For example, let's try to find the square root of 10. So we'll set down our number and our placeholder and our placeholder doesn't have to move. We'll take our guess, which will be 3, multiply guess by placeholder and add to dingva, multiply guess by dingva and subtract from the radicand, double the root and replace the dingva and shift. Now before we shift, it's convenient to put some placeholding zeros up. You can think about these additional zeros as being zeros placed after the decimal point. They're there to keep everything lined up. So our next digit will remember our guess times 60-something must be less than 100. So we guess 1, guess times placeholder and add to dingva, guess times dingva and subtract from the radicand, double the root so far, that's 62 and shift. Again, we'll guess, and whatever our guess is, our guess times 620-something must be less than 3,900. So we guess 6, guess times placeholder and add to dingva, guess times dingva and subtract from radicand, double and shift. And it's worth observing that we can keep going as far as we like to. But since the square root of 10 is some place between 3 and 4 and the digits of the root that we found are 3, 1, and 6, then we can read our partial root as 3.16. In other words, if we stop here, we'll have found the square root of 10 to two decimal places. Well, let's find the square root of 3 to, oh, I don't know, how about three decimal places? So we'll put down our root and our placeholder, and we don't need to move the placeholder. We guess 1 and go through our process. Guess times placeholder and add to dingva. Guess times dingva and subtract, double and shift. Our guess times 20-something must be less than 200, so we'll guess 9. Guess times placeholder and add to dingva. Guess times dingva and subtract. There's a problem here that's actually too much, which means that our next digit is lower than 9. So we've got to reset and guess lower. So let's guess 7. So our guess times placeholder and add to dingva. Guess times dingva is comfortably less than what we have, so now we can subtract, double the root, and shift. And we guess the next digit, whatever our guess is, times 340-something must be less than 1100, and so we guess about 3. So guess times placeholder and add to dingva. Guess times dingva and subtract, double and shift. Again, our guess times 3460-something must be less than 7100. So we guess 2 and go through our first pass. Guess times placeholder and add to dingva. Guess times dingva and subtract, double and shift. And so far we found the digits 1732, and so our approximate root is 1.732.