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how do I find the sq rt of a number like 163 that is not a perfect square
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Yolanda037

by Yolanda037 at February 09, 2011

we are working on determining if the points are collinear..here are my points P(9,6) Q (0,-3) R (3,1)

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ok so we can use Newton's method of square roots:im going to guess that 13 is the correct answer:so the formula is: x sub(n+1) = x sub(n) - ((f(xsub(n))-num)/f ' (xsub(n)))so f(x) is x^2 because we are trying to find what number squared = 163f '(x) is 2xso my original will be 13 - (13^2-163/(2*13)) = 13 - (169-163/26) = 13 - .230 = 12.769and 12.769 will be your next xsub(n)
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John_Doe John_Doe February 09, 2011

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Yolanda -I see you are an Algebra II student, so you probably don't have a clue what the previous solution meantI suggest something simple (if you don't have a calculator):(1) Find two perfect squares that "surround" your number. In your example:So 163 is surrounded by 144 & 169, agree? This means the square root of 163 must lie between 12 and 13, agree?(2) Determine where 163 falls within the range 144-169:There are 169-144 = 25 numbers in this range and 163 is 19 numbers beyond 144 so use 19/25 = 0.76.(3) Estimate of square root of 163 is:12 + 0.76 = 12.76.If you square this you get 162.8 ... not a bad estimate at all!Hope that helps
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Steve204 Steve204 February 09, 2011

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http://xw2k.nist.gov/dads/HTML/squareRoot.html This is the way we used to do it in the 60's if we had no tables, or slide rule.   When we got to enough decimal places precision,we stopped 
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kroo_jteague kroo_jteague February 09, 2011

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The only way I know to find out the square root of a number that is not a perfect square is either to simplify it, or use a calculator.I also don't know whether or not 163 can be simplified, but I'm pretty sure you can't simplify it any further.
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Gentou Gentou February 10, 2011

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