A **cubed** symbol is a symbol that is multiplied 3 times by itself. The **symbol/sign** for **cubed** is ³. This is moreover be called ‘a number **cubed**.

Let’s suppose to take an example -It is easy to say that the cube root of 27 is 3. However, it is not easy to type this in a human-readable format. You can use the formula editor in Microsoft Office or special applications such as Latex.

Unfortunately, using the formula editor in Word or Excel is tricky because the content will not be the same as the other text content in your document. Plus, you don’t need a formula editor to use it multiple times. If you want to introduce cube root characters into your documents, then an easy way is to use alt code keyboard shortcuts. In this article we give all information to write cube root in windows, mac, word/excel, and Latex.

The cubed symbol is denoted by ∛.

`∛`

`³`

When ^{3} = B, then A is the cube root of B, denoted **∛B = A**. For example, ∛9 = 3.

Contents

__The cubed symbol on Windows__

__The cubed symbol on Windows__

If your keyboard has a numeric keypad, then you can type the cubed symbol using an Alt code – this consists of you pressing a few numbers while holding the Alt key. The numeric keypad is to the right of your keyboard – most keyboards on the desk have a numeric keypad. If you are using a laptop, you will only see the numbers on the top row of the keyboard and not on the right. To type the cubed symbol on the keyboard, type **0179** while holding down the Alt key.

**³ =Alt+0179**

__Cubed Symbol on Mac__

__Cubed Symbol on Mac__

**³ ****=Option + 00B3**

Apple Mac OS or Mac book owners can use the** Option +00B3** keyboard shortcuts.

**Insert cubed symbol In Microsoft Word**

**0221b ➟ Alt + X = ∛**

Note: make sure “b” is a small letter.

Type the English letter “D” instead of the character. Select it and in the top menu on the** “Home”** tab set the font **“Symbol”**. The letter will automatically turn into a symbol for cubed.

Anywhere in the document, enter **“0221b”** and press the Alt and X hotkeys. The numbers are converted to a character. The keyboard layout must be English. **0221b ➟ Alt + X = ∛**

On a full keyboard with a right numeric keypad, you can use the following method. Hold Alt and type 0221b. It is necessary to enter numbers on the right digital block.

**The cubed symbol on Latex**

Here is the latex code for square root, cube root, and n^{th} root.

$\sqrt{x}$ \\ ,this is the format of square root in latex.

**$\sqrt[3]{x}$ \\ ,this is the format of cube root ****∛ in latex.**

$\sqrt[n]{x}$ \\ ,this is the format of n^{th} root in latex.

**Excel**

**How to type a cubed symbol in excel**

- Open an Excel file you need.
- Go to taskbar explore and type ‘character map’.
- Click on it to open. Select the cube symbol.
- Click on ‘Copy’.
- Right-click after the data you have to and click on ‘Paste’.

**Or**

- You can in addition use your keyboard to put a cube symbol.
- Press Alt along with type 0179 on your number keyboard.
- Now release the Alt key your symbol appears automatically.
- Please, make sure the NM Lock is on before entering the number combo.

**Find the cube root in Excel**

To calculate the cube root of a number in Excel, use the caret operator **(^)** with 1/3 as the exponent in a simple formula.

=number^(1/3)

In this example, the formula =D3^(1/3) is used to find the cube root of **1728**, which is** 12**.

__All in one information Table:__

Symbol | cubed |

Text | ∛ |

Alt Code | 0179 |

Windows Shortcut | Alt+0179 |

Mac Shortcut | Option + 00B3 |

MS Word Shortcut | 0221b ➟ Alt + X |

latex | $\sqrt[3]{x}$ \\ |

**Uses :**

In geometry, cube defines in geometry an object has all its side and faces which is equal in dimension. The cube symbol is also used in calculating the volume of the cube. The cube has the same side, height, and weight as 3d shape cube. Cube is also used in games like Ludo which is called dice and snake ladder. A cube number is a number that is multiplied by 3 times. For example, 2 cubed is 2³ = 2×2×2 = 8.

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**The Cube Root Symbol**

Cube root symbol: cube root symbol means it multiplies itself by 3 times.

You can use it like this: cube root 64 = 4(we say “the cube root of 64 equals 4”)

You Can Also Cube Negative Numbers

Have a look at this:

When we cube +3 we get +27: +3 × +3 × +3 = +27

When we cube −3 we get −27: −3 × −3 × −3 = −27

**Perfect Cubes**:

perfect cubes of a whole number.

0 0

1 1

2 8

3 27

4 64

5 125

6 216

7 343

8 512

9 729

10 1000

11 1331

12 1728

13 2197

14 2744

15 3375

It is simple to work away from the cube root of a perfect cube, but it is actually hard to work away from other cube roots.

### A Collection of Algebraic Identities

All the Algebraic Identities are derived from the Binomial Theorem, which is given as:

[latex] \mathbf{(a+b)^{n} =\; ^{n}C_{0}.a^{n}.b^{0} +^{n} C_{1} . a^{n-1} . b^{1} + …….. + ^{n}C_{n-1}.a^{1}.b^{n-1} + ^{n}C_{n}.a^{0}.b^{n}}[/latex]

Mostly Used Algebraic Identities list are given below:

(a + b)*Identity I:*^{2}= a^{2}+ 2ab + b^{2}(a – b)**Identity II:**^{2}= a^{2}– 2ab + b^{2}a*Identity III:*^{2}– b^{2}= (a + b)(a – b)(x + a)(x + b) = x*Identity IV:*^{2}+ (a + b) x + ab(a + b + c)*Identity V:*^{2}= a^{2}+ b^{2}+ c^{2}+ 2ab + 2bc + 2ca(a + b)*Identity VI:*^{3}= a^{3}+ b^{3}+ 3ab (a + b)(a – b)**Identity VII:**^{3}= a^{3}– b^{3}– 3ab (a – b)a*Identity VIII:*^{3}+ b^{3}+ c^{3 }– 3abc = (a + b + c)(a^{2}+ b^{2}+ c^{2}– ab – bc – ca)

**Few Examples**

**Example 1: Evaluate using algebraic identity (z+ 1)(z + 1) **

**Solution: **(z+ 1)(z+ 1) can be written as (z + 1)^{2}. Thus, it is of the form Identity I where a = z and b = 1. So we have,

(z + 1)^{2} = (z)^{2} + 2(z)(1) + (1)^{2 }= z^{2 }+ 2z + 1

**Example 2: Factorise using algebraic identity (m ^{4} – 1)**

**Solution: **(m^{4} – 1) is of the form Identity III where a = m^{2} and b = 1. So we have,

(m^{4} – 1) = ((m^{2})^{2}– 1^{2}) = (m^{2 }+ 1)(m^{2 }– 1)

The factor (m^{2 }– 1) factorized using Identity III where a = m and b = 1. So,

(m^{4} – 1) = (m^{2 }+ 1)((m)^{2 }–(1)^{2}) = (m^{2 }+ 1)(m + 1)(m – 1)

**Eample 3: Factorise 16t ^{2} + 4s^{2 }+ 9z^{2} – 16ts + 12sz – 24zt using algebraic identity.**

**Solution:** 16t^{2} + 4s^{2 }+ 9z^{2}– 16ts + 12sz – 24zt is of the form Identity V. So we have,

16t^{2} + 4s^{2 }+ 9z^{2} – 16ts + 12sz – 24zx = (4t)^{2} + (-2s)^{2} + (-3z)^{2} + 2(4t)(-2y) + 2(-2s)(-3z) + 2(-3z)(4t)= (4t– 2s – 3z)^{2} = (4t – 2s – 3z)(4t – 2s – 3z)