# What Is The Method For Computing The Square Root Of 169?

Take Least Common Multiplier (commonly referred as LCM) of 169.

Start dividing 169 by 2, 3, 4, 5, ... Carry on dividing until 169 is divisible completely. By completely, I mean to say that the end result must be a whole number and not a decimal fraction or you can say that we are looking for a divisor. (For example; 6 is completely divisible by 2 as 2x3 = 6. Here both 2 and 3 are divisors of 6)

Well while searching for a divisor for 169, you discard 2, 3, 4, .., 11, 12 on your way through and finally come across 13 which is the only number that divides 169 completely or a divisor of 169. Now 13 multiplied by which whole number results in 169? Your answer again is 13. I.e. 13x13 = 169.

In order to find square root, one has to multiply two same numbers. Hence in this case, it is obvious that 13x13 = √169. Thus, square root of 169 comes out to be 13.
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The way I was taught is described very well by the National Institute of Standards and Technology (NIST) at www.nist.gov
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Oddman commented
Thanks. That's the way I learned it, too. I tried to respond to a question along the same lines, but after my answer was posted, I found the question had been disapproved. Apparently, too many people had responded that the square root was 13, and some admin thought it was repetitive. (sigh)
Mark Mottian commented
Plus or minus 13
Isn't it usually the biggest number that can be multiplied by itself to get the number 13 X 13=169 or the biggest number that can divide into the number without a remainder.169/13=13...am I wrong or right
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Oddman commented
Apparently, you did not read the question. The answer to the question is a description of an algorithm. Yes, trial and error is an algorithm, but it is only really useful for small integers. A more general solution is needed.
169 divided by 13 = 13 {without a remainder}   ♥nassy
and 13 multiplied by itself = 169
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Oddman commented
How did you identify that 13 should be the number you divide by?
#1: 100% useful, but often takes a great deal of timeYou can, of course, use trial and error by making successive guesses.  Experience, as is known, can help whittle down the range and iteration can reduce the list.

#2: About 70% useful, less if the
A second means of establishing this square root might be to use the following algorithm:
0. Attempt reduction with known primes and other well-known values
(division by 2 is easy, as are 3, 4, 5, 6, 7, 8, 9, 10, 11, and 16)
1. Establish the length of the value (in your case, 3); subtract one (in your case, 2)
2. Divide the original value by this number (169/2 = 84.5)
3. Generate complete list of primes less than or equal to this number
(trivial but time consuming: 2, 3, 5, 7, 11, 13, 17, 19, 23, 27, 31, 37, 41, etc)
4. Divide each until reducing. Or not.

#3: 100% useful, takes less time, non-traditional
A genuinely distinct alternative may be found in the Tractenberg method.  His text is available here: www.scribd.com; square roots start on page 169, but I'd certainly recommend starting either at the beginning of the chapter (page 185) or reading the book up to that point; in brief, the heuristic is to use the form of the number to estimate the approach (three digits/four digits, what the leading digit is) and use a collection of rules to further break it down.

Initially learning it takes a bit of time, but it is far more consistently useful than the traditional way (which I learned as well).  And, because the technique is consistently independent of the size of the number, in my opinion becomes ridiculously more useful as numbers get larger.
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Wow you guys make me feel really uneducated...I was going to say use a calculator but ok...that may be why I'm still in schoolXD hahah
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Shannon commented
Same, calculators are easy. 