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	PlanetMath: cube root
		The cube root operation is distributive for multiplication and division, but not for addition and subtraction.
		The cube root is a special case of the general nth root.
		This is version 8 of cube root, born on 2001-11-10, modified 2006-06-21.
	planetmath.org /encyclopedia/CubeRoot.html (140 words)

	Cube root - Wikipedia, the free encyclopedia
		For example, the cube root of 8 is 2, because 2 × 2 × 2 = 8.
		The cube root operation is associative with exponentiation and distributive with multiplication and division, but is not associative or distributive with addition or subtraction.
		This means that in polar coordinates, we are taking the cube root of the radius and dividing the polar angle by three in order to define a cube root.
	en.wikipedia.org /wiki/Cube_root (595 words)

	How to Do Cube Roots of 9 Digit Numbers in Your Head
		When I say "the cube root of numbers like 283593393", there is of course something special about 283593393, which is that it is a cube of a whole number, so it's cube root is a whole number.
		The cube root of a 6 digit number has to be less than 100, so you could consider memorising the first 100 cubes.
		Using the same techniques, we can easily calculate the first and last digits of the cube root of a 9 digit number (assuming, as already stated, that it is known to be the cube of a whole number).
	www.1729.com /blog/CubeRoots.html (1338 words)

	算盤 Cube Root - Abacus Arithmetic by Welton J. Crook (Site not responding. Last check: 2007-10-26)
		The extraction of the cube root of a number on the abacus is more complicated but not more tedious than the extraction of the square root.
		Subtract the sum of the "square" number from the residue of the "cube" number and repeat the process given in (f) and (g) until the number in the first group of the "cube" number is less than the "square" number.
		The situation on the abacus is shown in Figure 34, in which, numbering the columns from the left, the "root" number, 61, occupies columns one and two; the "square" number, 1261, occupies columns five, six, seven and eight; the "cube" number, 1261, occupies columns ten, eleven, twelve and thirteen.
	webhome.idirect.com /~totton/soroban/cuberoot.html (887 words)

	SparkNotes: Powers, Exponents, and Roots: Square Roots
		The square root of a number is the number that, when squared (multiplied by itself), is equal to the given number.
		A cube root is a number that, when cubed, is equal to the given number.
		The 4th root is denoted by an exponent of "1/4", the 5th root is denoted by an exponent of "1/5"; every root is denoted by an exponent with 1 in the numerator and the order of root in the denominator.
	www.sparknotes.com /math/prealgebra/powersexponentsroots/section4.rhtml (640 words)

	Cube (arithmetic) - Wikipedia, the free encyclopedia
		A perfect cube (also called a cube number, or sometimes just a cube) is a number which is the cube of an integer.
		With even cubes, there is considerable restriction, for only 00, o2, e4, o6 and e8 can be the last two digits of a perfect cube (where o stands for any odd digit and e for any even digit).
		Some cube numbers are also square numbers, for example 64 is a square number (8 × 8) and a cube number (4 × 4 × 4); this happens if and only if it is a perfect sixth power.
	en.wikipedia.org /wiki/Perfect_cube (618 words)

	Cube - Search Results - MSN Encarta
		Cube, in mathematics, a solid three-dimensional geometric figure bounded by six planes; each of the six sides or faces of a cube is a square (see...
		Root (mathematics), in mathematics, either: a number that when multiplied by itself a stated number of times yields as a result a second, given...
		To divide a cube into two other cubes, a fourth power or in general any power whatever into two powers of the same denomination above the second is...
	uk.encarta.msn.com /Cube.html (185 words)

	#1 Site For Learning Mathematics
		The reverse of squares or cubes is called square roots or cube roots.
		Cube root of a positive number will always be a positive number.
		If you know the volume of the cube, you will be able to determine the length of the side of the cube by using the cube root of the volume.
	home.att.net /~cat5a/sq_cub_roots.htm (552 words)

	CUBES ROOTS OF NUMBERS (Site not responding. Last check: 2007-10-26)
		The cube root of a number is the number when multiplied by itself twice, equals to the given number.
		To find the cube root a decimal, express the decimal into cub of a decimal or change it into a fraction.
		We can estimate the value of the cube root of a number by approximation of by determining the range.
	www.freewebtown.com /telekomunikasi/cuberoots.htm (276 words)

	Cube root
		In mathematics, the cube root of a number is a number which, when cubed (multiplied by itself and then multiplied by itself again), gives back the original number.
		For instance, the cube roots of unity are 1, (− 1 + √3i)/2 and (− 1 − √3i)/2.
		If R is one cube root, the other two cube roots can be found by multiplying R by the two complex cube roots of unity.
	www.askfactmaster.com /Cube_root (272 words)

	9_1classnotes
		A cube root is a number that when cubed is equal to a given number or to a given radicand in a radical expression.
		The cube roots of positive radicands are positive and the cube roots of negative radicands are negative.
		For square roots and for cube roots, we have seen that when the power of a factor in the radicand is equal to the index of the radical, then the root is equal to the factor itself.
	mtsu32.mtsu.edu:11237 /9_1classnotes.htm (538 words)

	Cube and Higher Roots (Site not responding. Last check: 2007-10-26)
		The algorithm was derived by an examination and extension of the algorithm for finding square roots by estimation and averaging with which many readers may be familiar and which is, in fact, merely a special case of the general algorithm.
		To begin with, let us estimate the cube root to be 6, which is purposely lower than the better estimate of 7 in order to emphasize how quickly convergence is obtained even with a very poor estimate.
		Subsequent iterations result in revised estimates of 7.697141 and finally 7.697002, which, in fact, is the closest approximation of the cube root obtainable on a common four-function calculator.
	www.geocities.com /ehydrogen/cuberoots.html (515 words)

	Square Roots (Site not responding. Last check: 2007-10-26)
		The square root of the number two is found by raising 10 to the power of (1/2)log(2) which produces 10^.1505 or 1.4142.
		Their technique goes as follows: The number to have the root determined of is a and the root of this number is x.
		The cube root of the number is x, x = a+b+c, while a, b, and c are any digit between 0 and 9.
	home.earthlink.net /~sondybeamer/homework/algebra/roots/root.html (1150 words)

	Nth root Summary
		The principal nth root of a real number a is the unique real number b that is an nth root of a and is of the same sign as a.
		The nth roots of unity are of particular importance.
		It was once conjectured that all roots of polynomials could be expressed in terms of radicals and elementary operations.
	www.bookrags.com /Nth_root (1273 words)

	CubeRoots - Mentat Wiki
		Once you know the one-digit cubes and their roots, and can remember which ending digit in a cube refers to which digit of its cube root, you're ready to move on to the next section.
		This means that the cube root of 148,877 is 53.
		The closest cube to 4 without going over is 1 (which has a cube root of 1).
	www.ludism.org /mentat/CubeRoots (455 words)

	Cube roots (Site not responding. Last check: 2007-10-26)
		My son is in 4th grade and needs to simplify the cube roots of 216, 512 and 64.
		Multiplying 5x5x5 = 25x5 = 125 shows that the cube root of 64 is less than 5 and the cube roots of 216 and 512 are larger than 5.
		You know that both cube roots are larger than 5 and smaller than 10 so try one of 6, 7, 8 and 9.
	mathcentral.uregina.ca /QQ/database/QQ.09.01/kathy1.html (187 words)

	10.1: Radical Expressions (Site not responding. Last check: 2007-10-26)
		In other words, a principal square root is the positive root (except in the case of zero because the principal square root of zero is zero.).
		The square root symbol represents the principal root.
		The cube root is written with a radical symbol with an index of 3.
	www.mtsu.edu /~mhiggs/101.html (463 words)

	cube root
		Calculation of a cube root by hand is a little like long-hand division or manual square root.
		That is, we have improved our knowledge of the square root by one digit, B. We take whatever remains, scale again by 1000, by bringing down three more digits, and repeat the process.
		Note: In computers and hand-held calculators, square root, sine, cosine, and other transcendental functions are calculated with sophisticated functions based on the Newton-Raphson method, sometimes called Newton's method.
	www.nist.gov /dads/HTML/cubeRoot.html (760 words)

	Math Forum - Ask Dr. Math Archives: High School Square/Cube Roots (Site not responding. Last check: 2007-10-26)
		That seems to indicate that the square root of 11 is a rational number, but it's not.
		Examine both the units digits and the digital roots of perfect squares to help determine whether or not a given number is a perfect square.
		Is the Square Root of i^4 Equal to 1 or -1?
	mathforum.org /dr.math/tocs/squareroot.high.html (959 words)

	Cube Root Extraction Method in the Nine Chapters
		Suppose we want to find the cube root of a number N. Let x^2 = N. Let x = a + b + c where a is the hundreds position of the root, b is the tens position of the root, and c is the units position of the root.
		The cube root of N has been found.
		When extracting (cube) root, the above formula is reserved.
	www.math.sfu.ca /histmath/China/1stCenturyAD/NineCubeRoot.html (492 words)

	Roots and Radical Expressions
		The principal square root of a non-negative number is its nonnegative square root.
		The cube root of a positive number is positive.
		The cube root of a negative number is negative.
	www.jcoffman.com /Algebra2/ch7_1.htm (529 words)

	Example 1
		The term ”square root” comes from the fact that a square root is in some sense the “opposite” of squaring a number.
		Since squaring a number would give you the area of a square, the square root of the area of a square is the length of a side of that square.
		We choose the output for a square root to be a positive number (or zero, in the case of the square root of zero).
	www.sscc.edu /home/jdavidso/math118/Chapter7/Section7.1/example1.html (569 words)

	Hints for solving the problems
		Perfect cubes are numbers that when you take the cube root of it you get a whole number.
		Remember when a perfect cube as, a number, is under the radical, take the cube root of it, but when a number, whether it is a perfect cube or not, is under the radical as an exponent of a variable, take 1/3 of it.
		The factored form (the ans.) is: the square root of the first term + the square root of the second term times the square root of the first term – the square root of the second term.
	fp.academic.venturacollege.edu /rbrunner/hints_7.3.htm (937 words)

	Algebra II: Powers and Roots - Math for Morons Like Us
		However, the principal square root of a real number is its nonnegative square root (8 would be the principal square root of 64).
		Although you usually see only square and cube roots, it is possible to see and use 4th, 5th, and 6th roots of numbers.
		N-th roots, like square roots have a special rule when the index is the same as the power the radicand is raised to.
	library.thinkquest.org /20991/alg2/pr.html (1233 words)

	01.15.98 Algorithm extracts cube root
		After calculating the cube root, the routine prints the result on the screen.
		So, with error set to 0.00001, the accuracy is about 0.003% for the cube root of 0.1, 0.03% for the cube root of 0.01, 0.3% for the cube root of 0.001, and so forth.
		In the limit--the cube root of 0--you can't divide by 0 to find percent accuracy, but the actual root that the program calculates is 0.0156250.
	www.edn.com /archives/1998/011598/02di_04.htm (605 words)

	Cube roots via mediants
		But c'/a', a'/b', and 2b'/c' approach the cube root of 2 after a large number of iterations.
		This means the entries in the matrix after a few iterations will increase by a factor of the cube root of 2 vertically.
		In other words, the approximation of the cube root of 2 is the quotient of any two consecutive entires vertically or horizontally.
	www.mathpath.org /Algor/cuberoot/cube.root.mediant.htm (211 words)

	Intermediate Algebra Tutorial on Rationalizing Denominators and Numerators of Radical Expressions
		One example of an irrational number is when you have a root of an expression that is not a perfect root, for example, the square root of 7 or the cube root of 2.
		If the radical in the denominator is a cube root, then you multiply by a cube root that will give you a perfect cube under the radical when multiplied by the denominator and so forth...
		If the radical in the numerator is a cube root, then you multiply by a cube root that will give you a perfect cube under the radical when multiplied by the numerator and so forth...
	www.wtamu.edu /academic/anns/mps/math/mathlab/int_algebra/int_alg_tut41_rationalize.htm (1870 words)

	Cube And Cube Root Calculator
		This calculator is designed to give the cube and cube root of any number.
		In certain cases, as is the case with mainframes and minicomputers, our calculation of the cube root is a very close approximation.
		Both the cube and cube root values are calculated.
	www.csgnetwork.com /cuberootcubecalc.html (73 words)

	Duplicating the Cube
		The problem is to find a cube equal in volume to twice a given cube, or in other words, if the edge of the given cube is one, find a line equal in length to the cube root of two.
		That means if you use 63/50 to duplicate a cube a meter on a side, the duplicate will be accurate to within 0.008 cm or 0.08 millimeters, or 0.003 inches, about the thickness of a sheet of paper.
		AD is the edge of the doubled cube (AD = AO times cube root of two).
	www.uwgb.edu /dutchs/PSEUDOSC/DuplCube.HTM (531 words)

	simplifying cube root fractions
		The square rootsign: is called the root symbol.
		The number inthe v of the radical is called the index number or root number.
		The above reads the cube root of -8 is -2.
	www.softmath.com /tutorials2/simplifying-cube-root-fractions.html (704 words)

	cube root definition - Dictionary - MSN Encarta
		cube root definition - Dictionary - MSN Encarta
		Search for "cube root" in all of MSN Encarta
		base number of cube: a number or quantity that, when multiplied by itself twice, equals a given number or quantity
	encarta.msn.com /dictionary_1861694340/cube_root.html (83 words)

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