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# how to find the square root of 361

Question:Well, so I have my finals coming up and unfortunately I forgot how to find square roots using Newton's Method. Now, when you're explaining, I don't want any of this: "First, here's the divide-and-average algorithm. Suppose that you wish to calculate the square root of a number A. The divide-and-average algorithm is: 1. Choose a rough approximation G of sqrt(A). 2. Divide A by G and then average the quotient with G, that is, calculate: G* = ((A/G)+G)/2 3. If G* is sufficiently accurate, stop. Otherwise, let G = G* and return to step 2." Really. Please. Just explain it simply. I remember something about making an estimate of what the square root would be, and dividing, and there was lots of long division. If you tell me about extracting square roots, or if you give me some long scientific google-searched page that only some old nerdy hermit would understand, I will personally force you to eat 70 lemons. Thank you.

Answers:Start from a number that's close to the square root you're looking for. Pick a number that squares to something close to your original number. (for example, if you're looking for the square root of 220, you would do well to choose 15, which squares to 225). We take that and plug it into our formula, and a new number comes out. We plug that number into the formula, and another number comes out. Keep doing it until the number that comes out is the same as the one that went in (when rounded to the precision you want). Unfortunately, the formula isn't as simple as averaging. So, we have our guess, 15. That's x0 To get our next approximation, x1, we take x0 - (x0^2 - 220)/2x0, so we have x1 = 15 - (225 - 220)/30 = 15 - 5/30 = 14.8333333 (carry it out to one more digit than you want in your final approximation). To find our next approximation, x2, we do the same thing again: x2 = x1 - (x1^2 - 220)/2x1 = 14.8333333 - (14.8333333^2 - 220) / 29.6666666 And we keep going until the new approximation is the same as the old one.

Question:WITHOUT using estimation or a calculator, how can I find the square root of a number that is not a perfect square? example: how can you find the square root of a number like 12.385?

Answers:I had learned a method of finding the square root of a number. You can look up Van's Algebra, or similar books for details. Use Yahoo search of 'square root of '.

Question:I'm not sure how to find this derivative... It's 1 - (the square root of x) Please help :\

Answers:Rewrite sqrt(x) as x^(1/2) and you can use the power rule as usual.

Question:of a number that doesn't have a perfect square root. (it would be a decimal) i also need to know how to find the square root of ANY number without a calculator. i dont know how to do it.

Answers:This site explains three different ways to do it: http://www.homeschoolmath.net/teaching/square-root-algorithm.php