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# how to find the square root of 225

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:thise comes from :the surface area formula: S=(pi)(r) (square root of r^2 + h^2) where the h=5 and s=100 how do i solve for r ??? please include steps to follow, thanks!!!

Answers:100= r (r +25) Square both sides: 10,000= r (r +25) Distribute: 10,000= r +25 r Divide by : 10,000/ = r +25r Add 625/4: 10,000/ + 625/4 = r + 25r + 625/4 Factor right side: 10,000/ + 625/4 = (r +25/2) Take the square root of both sides: (10,000/ + 625/4) = r +25/2 Subtract 25/2: r = -25/2 (10,000/ + 625/4) Take the square root again: r= (-25/2 (10,000/ + 625/4)) This gives your four possible solutions for the radius. However, note that if the sign on the inner square root is negative, you will get an imaginary solution, which in the context of radii is nonsensical. Similarly, the sign on the outer square root is also not negative, because that would mean you have a negative radius, which is also nonsensical. Thus your solution is: r= (-25/2 + (10,000/ + 625/4))

Question:So am studying for my GED and this shit is in this GED book I have. Am not understanding how to do this. All through school we used a calculator with square roots so this is new to me. What is the easiest way to do this? Thanks! Lets say whats the square root of 50 for example.....

Answers:lets say the value is 5. You want to calculate its square root. pick the closest perfect squares around it 2 = sqrt(4) 3 = sqrt(9) so, try a value in between, like 2.5, it lies half way between 2 and 3 2.5*2.5 = 6.25, so that's close but we can get closer. try a value half way between 2.5 and 2. try 2.25 2.25*2.25 = 5.06, that's pretty close but if its not close keep zeroing in on the value and testing its square until its as close to 5 as you want. 50 7*7 = 49 8*8 = 64 this is so close to 50, we know its close to 7 7.1*7.1 = 50.41 so try 7.05*7.05 = 49.7 so try 7.075*7.075 = 50.06 so that's close Alternate method: 50 = 25*2 = 5*sqrt(2) so, if you know the values of sqrt(2), sqrt(3), sqrt(5), etc. often times large numbers can be factored into a perfect square and so other factor. so 5*sqrt(2), if you know that sqrt(2)=1.414 you can do the arithmetic directly.

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 '.

How to find the square root of a number? :This video will show you how to find the square root of any number. Thanks for learning :) www.i-hate-math.com

MF49: How to find a square root :We consider three methods, or algorithms, for finding the square root of a natural number we know to be a square. One is trial and error estimation, the other is the Babylonian method equivalent to Newton's method, and the third we call the Vedic method, since it goes back to the Hindus. It is completely feasible to do by hand. This video belongs to Wildberger's MathFoundations series, which sets out a coherent and logical framework for modern mathematics.