This is not the document you are looking for? Use the search form below to find more!

Report

# Cubes and Cube Roots

Document Description
In arithmetic and algebra, the cube of a number n is its third power — the result of the number multiplied by itself twice: n3 = n × n × n. This is also the volume formula for a geometric cube with sides of length n, giving rise to the name. The inverse operation of finding a number whose cube is n is called extracting the cube root of n. It determines the side of the cube of a given volume. It is also n raised to the one-third power. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 23 = 8 or (x+1)3. A perfect cube (also called a cube number, or sometimes just a cube) is a number which is the cube of an integer.
File Details
• File size: 176.38kb
• Pages: 3
• Tags: cubes and cube roots, 2 digit division with remainders, convert a whole number to a fraction
• content preview
Submitter
Embed Code:

Related Documents

## Chart, Squares, Cubes, And Square Roots From Number 1 To 20

by: ghaith, 1 pages

numbersquarecubesquare root of number1111.0002481.41439271.732416642.0005251252.2366362162.4497493432.6458645122.8289817293.0001010010003.1621112113313.3161214417283.4641316921973 ...

## Histochemical Aspects of Penetration and Vascular Connection of Broomrape Haustoria in the Host Root, and the Possible Implication of Phenylpropanoids

by: shinta, 5 pages

Penetration of haustorial cells of Broomrape (Orobanche spp.) was studied in the root tissues of pea (Pisum sativum L.). It was similar in a number of other hosts (faba bean, tomato, Indian ...

## THIN- LAYER DRYING OF DICED CASSAVAROOTS

by: shinta, 7 pages

Fresh cassava (Manihot spp) roots were obtained from a farm and used in this study. They were peeled and diced using a special dicing machine into cubes of side 0.5 cm. The cubes were ...

## The Effects of Boiling and Leaching on the Content of Potassium and Other Minerals in Potatoes

by: shinta, 7 pages

The white potato (Solanum tuberosum L.) is a valuable source of potassium in the human diet. While most consumers benefit from high levels of potassium in potato tubers, individuals with ...

## ISLAMIC BANKINGAND FINANCE: GROWTH ANDCHALLENGES AHEAD

by: monkey, 9 pages

With conventional brick and mortar roots going back to the 1960’s and Quran teachingsdating back nearly 1,500 years, Islamic banking is both an established school of thoughtand a relatively ...

## Remy Lace Wigs

by: houstonhollo1128, 1 pages

There is a whole lot of mis-facts going all-around regarding Remy lace wigs and non-Remy lace wigs. This post will try to obvious up the confusion. Initially of all a Remy wig is one that is ...

by: mahesh4528, 3 pages

Quadratic Formula solver is a polynomial equation of second degree. The general form of a quadratic equations is ax2+bx+c = 0. The contributions of the ancient Indian Mathematicians to quadratic ...

## How to Solve Quadratic Equations

by: mahesh4528, 3 pages

How to Solve Quadratic Equations is a polynomial equation of second degree. The general form of a quadratic equations ax2+bx+c = 0. The contributions of the ancient Indian Mathematicians to ...

by: storysubmission11, 5 pages

Quadratic Equation is a polynomial equation of second degree. The general form of a quadratic equations is ax2+bx+c = 0. The contributions of the ancient Indian Mathematicians to ...

by: storysubmission11, 5 pages

Quadratic Equation is a polynomial equation of second degree. The general form of a quadratic equations is ax2+bx+c = 0. The contributions of the ancient Indian Mathematicians to ...

Content Preview
Cubes and Cube Roots
Cubes and Cube Roots
In arithmetic and algebra, the cube of a number n is its third power -- the result of the number
multiplied by itself twice:
n3 = n x n x n.
This is also the volume formula for a geometric cube with sides of length n, giving rise to the name.
The inverse operation of finding a number whose cube is n is called extracting the cube root of n. It
determines the side of the cube of a given volume. It is also n raised to the one-third power.
The cube of a number or any other mathematical expression is denoted by a superscript 3, for example
23 = 8 or (x+1)3. A perfect cube (also called a cube number, or sometimes just a cube) is a number
which is the cube of an integer.
If a and b are two natural numbers such that a3 = b, then b is called the cube of a. If the units digit of
a3 is b, then the cubes of all numbers ending with a will have their units digit as b. The cubes of all
numbers that end in 2 have 8 as the units digit. The cubes of all numbers that end in 3 have 7as the units
digit. The first odd natural number is the cube of 1. The sum of the next two odd natural numbers is the
cube of 2. The sum of the next three odd natural numbers is the cube of 3, and so on.
Know More About :- 2 Digit Division with Remainders

Math.Edurite.com
Page : 1/3

The cube root of a given number is a number, which, when multiplied with itself three times, gives the
number. If a given number is a perfect cube, then its prime factors will always occur in groups of three.
The cube root of a number can be found using the prime factorisation method or estimation method.
Cubes in number theory ;- There is no smallest perfect cube, since negative integers are included. For
example, (-4) x (-4) x (-4) = -64. For any n, (-n)3 = -(n3). Unlike perfect squares, perfect cubes do
not have a small number of possibilities for the last two digits. Except for cubes divisible by 5, where
only 25, 75 and 00 can be the last two digits, any pair of digits with the last digit odd can be a perfect
cube. 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 x 8) and a cube number (4 x 4
x 4); this happens if and only if the number is a perfect sixth power. It is, however, easy to show that
most numbers are not perfect cubes because all perfect cubes must have digital root 1, 8 or 9.
Moreover, the digital root of any number's cube can be determined by the remainder the number gives
when divided by 3:
If the number is divisible by 3, its cube has digital root 9;
If it has a remainder of 1 when divided by 3, its cube has digital root 1;
If it has a remainder of 2 when divided by 3, its cube has digital root 8.
Waring's problem for cubes ;- Every positive integer can be written as the sum of nine (or fewer)
positive cubes. This upper limit of nine cubes cannot be reduced because, for example, 23 cannot be
written as the sum of fewer than nine positive cubes:
23 = 23 + 23 + 13 + 13 + 13 + 13 + 13 + 13 + 13.
Fermat's last theorem for cubes ;- The equation x3 + y3 = z3 has no non-trivial (i.e. xyz 0)
solutions in integers. In fact, it has none in Eisenstein integers.
Both of these statements are also true for the equation[2] x3 + y3 = 3z3.

Math.Edurite.com
Page : 2/3

ThankYou
Math.Edurite.Com

# Document Outline

• ﾿

Cubes and Cube Roots

Share Cubes and Cube Roots to:

example:

http://myblog.wordpress.com/
or
http://myblog.com/

Share Cubes and Cube Roots as:

From:

To:

Share Cubes and Cube Roots.

Enter two words as shown below. If you cannot read the words, click the refresh icon.

Share Cubes and Cube Roots as:

Copy html code above and paste to your web page.