what is the easiest way to find the square root of a number with out a calculator?
342569
divide by a number and get the same number you are dividing by as an answer for example  \n49 divided by 7 =7
1060817
Square Root:\n\nSQRT(1839472)=1356.271\n\nSQRT(75639)=275.0255\n\nSum:\n\nSQRT(1839472) + SQRT(75639)\n\n= 1631.2964 (ans)
283638
sqrt(25)=5 or -5. To verify it:\n\n5*5=25 checks\n-5*-5=25 checks\n\nboth work.\n\nan important thing to remember while square-rooting a number is that the root can be both positive or negative, as two negatives multiply up to a positive.
909546
The square root of a number is just the number which when multiplied by itself gives the first number. So 2 is the square root of 4 because 2 * 2 = 4.\n\nStart with the number you want to find the square root of. Let's use 12. There are three steps:\n\n   1. Guess\n   2. Divide\n   3. Average.\n\n      ... and then just keep repeating steps 2 and 3. \n\nFirst, start by guessing a square root value. It helps if your guess is a good one but it will work even if it is a terrible guess. We will guess that 2 is the square root of 12.\n\nIn step two, we divide 12 by our guess of 2 and we get 6.\n\nIn step three, we average 6 and 2: (6+2)/2 = 4\n\nNow we repeat step two with the new guess of 4. So 12/4 = 3\n\nNow average 4 and 3: (4+3)/2 = 3.5\n\nRepeat step two: 12/3.5 = 3.43\n\nAverage: (3.5 + 3.43)/2 = 3.465\n\nWe could keep going forever, getting a better and better approximation but let's stop here to see how we are doing.\n\n    3.465 * 3.465 = 12.006225\n\nThat is quite close to 12.
408683
When we square a number we multiply it by itself\n\nThe square root of a number is the number that when multiplied by itself makes that number.\n\nFor example:\n\nThe square root of 9 is 3 (3 * 3 = 9)\n\nThere are different ways of finding the square rot of a number (by hand - using a calculator is just too easy lol) and the source below shows you some of them.
1122465
Just plug in 1 for x.\n√(1-1) = √0 = 0
709225
Finding the square root\n\nClick on the URL below for additional information concerning finding the roots without a caculator\n\nwww.nist.gov/dads/HTML/squareRoot.html \n\nwww.homeschoolmath.net/teaching/square-root-algorithm.php \n\n- - - - - - -s-
412542
x = -b +(or)- sqrt(b^2 - 4ac)\n    -------------------------\n               2a
24161
The square root of a negative number is an imaginary one.  The square root of -1 is known as i.  Negative square roots work out like positive ones, only with the i, so SqRoot(-4) = 2i and SqRoot(-64) = 8i.
737774
You figure the square root of each number separately...you've probably learned that in class alredy (how to do that)...then you take reach result, and multiply them together for your final answer.\n\nUse your textbook for reference...good luck!
416099
The simplest, but most tedious, way to calculate the decimal digits of a square root is to figure out each digit in turn, as follows. \nFirst of all, find how many digits to the left of the decimal point your square root will have. \n\nA number with one digit to the left of the decimal point will be somewhere from 1 up to, but not including, 10; therefore, its square will be somewhere from 1 up to, but not including, 100, and hence will have either one or two digits to the left of the decimal point. \n\nA number with two digits to the left of the decimal point will be somewhere from 10 up to, but not including, 100; therefore, its square will be somewhere from 100 up to, but not including, 10000, and hence will have either three or four digits to the left of the decimal point. \n\nAnd so on. \n\nTherefore, if the number you're trying to find the square root of has one or two digits to the left of the decimal point, its square root will have one; if it has three or four, its square root will have two; and so on. \n\nNow, having found how many digits the square root has, just start from the left and figure out each digit in turn. \n\nFor example, to find the square root of 1234 to 3 decimal places: \n\nThe square root has two digits to the left of the decimal point, so we're looking for a number of the form AB.CDE. . . (and we want to find A through E). \n\nNow, 10^2=100, 20^2 = 400, 30^2=900, all too small, but 40^2=1600, too big. This tells us the first digit A is 3. \n\nNext, 31^2 = 961, 32^2 = 1024, 33^2 = 1089, 34^2=1156, 35^2 = 1225, all too small; 36^2 = 1296, too big, so the second digit B is 5. \n\nThirdly, 35.1^2 = 1232.01, too small, but 35.2^2 = 1239.04, too big, so the third digit C is 1. \n\nAnd so on; continuing in this way, you see that . \n\nThis method is horribly slow and inefficient but that's no problem in an era of calculators. All the necessary ideas are there. \n\nYou can apply lots of little shortcuts to this procedure to drastically reduce the number of computations you need to do. Then you come up with a procedure similar to the long-division algorithm. Its complicated to remember, though; I don't remember it offhand. It is seldom taught today because there is little need for it. \n\nTo actually calculate a square root to a large number of digits quickly, one uses a different method. For example, saying that x^2 = a is the same as saying x = (1/2)(x + a/x) and you can use this as the basis of an iteration. Start with one value of x, for example, x=1. Then get a second value y = (1/2)(x + a/x). Then get a third value z = (1/2)(y + a/y). And so on. It turns out that these numbers x, y, z, . . . converge quite quickly to the desired square root, especially if you start with a number that is already close. \n\nDoing this calculation in the above example, for a=1234, and starting with the number a=40 which is obviously just a little bit bigger than the desired square root, you get the numbers 40, 35.425, 35.129578. . . , 35.128336. . . , 35.128336. . . and you see that just four calculations are enough to get the square root accurate to six decimal places.
26092
The Babylonian method is easy and fast:\n\nn[i+1] = (n + (r/n))/2\nwhere n is the approximate root, and r is the number you wish to find the sqaure root of. Check sources for more info.
538847
For any quadratic of the form ax^2 + bx + c = 0, the roots are\n\nx = (-b +/- sqrt(b^2-4ac)) / 2a\n\nSqrt here is shorthand for "the square root of".
978895
Can you use a square root symbol?  If so, sqrt(9) + 9 - 9
832512
either square root or erauqs
858418
Click ON\nClick PRGM\nSelect NEW tab and hit ENTER\n\nTo select DISP and PROMPT:\n Hit PRGM when creating or editing a program,\n Select Tab I/O and you will see you selection\n\nTo get the arrow, click STO-> just to the left of 1\n\n\nThis is the Program: (or the one I use)\n\n:Disp "AX^2+BX+C"\n\n:Prompt A\n:Prompt B\n:Prompt C\n:(-B+*square root*(B^2-4AC))/(2A)->D\n:(-B-*square root*(B^2-4AC))/(2A)->E\n:Disp D\n:Disp E\n\nTo run program, go to the main screen, click PRGM, select your program, hit ENTER, input values for A, B, and C, hit ENTER and you result will show your two possible answers.
998294
square root of 13 is the answer