# Cube Root of 64

The cube root of 64, denoted as 364. The Cube root of 64 is the number which multiplied by itself three times gives the product as 64. Since 64 can be expressed as 2*2*2*2*2*2. Therefore, the cube root of 64 = 3 2 2 2 2 2 2 = 4

## What is Cube Root ?

The cube root of a number is a value that represents the number that, when multiplied by itself three times, gives the original number. In other words, it's a number that, when raised to the power of 3, gives the original number. For example, the cube root of 27 is 3, since 3 3 3 = 27. The cube root of a number is denoted using the symbol.

### Cube Root Symbol

The symbol for the cube root of a number is 3 . For example, to indicate that x is the cube root of a number n, we write x=3n .

### Perfect cube

A perfect cube is a number that is the result of multiplying an integer by itself three times. In mathematical terms, a number n is a perfect cube if there exists an integer x such that x3=n .

**For example, the first few perfect cubes are:**

13 |
1 |

23 |
8 |

33 |
27 |

43 |
64 |

53 |
125 |

63 |
216 |

73 |
343 |

83 |
512 |

93 |
729 |

103 |
1000 |

and so on.

### Non Perfect Cube

A non-perfect cube is a number that is not a perfect cube, meaning it cannot be represented as the result of an integer raised to the power of 3. For example, 7 is a non-perfect cube because there is no integer value of x such that x3=7 .

The cube root of a non-perfect cube number is not an integer, and can be either a rational or an irrational number. To find the cube root of a non-perfect cube, you can use the estimation and refinement method, However, it's important to note that finding an exact value for the cube root of a non-perfect cube is not always possible, and the answer will typically be an approximation to a certain number of decimal places.

### How to Find Cube Root?

There are different methods to find the cube root of a number, but one common method is the estimation and refinement method:

- Estimate the value: Find the nearest perfect cube to the number and use that as the estimate for the cube root.
- Refine the estimate: Use the formula, (x+n/x2)/3 where x is the estimate and n is the original number.
- Repeat step 2: Keep refining the estimate until you have an answer that is accurate to the desired level of precision.

### Prime Factorization Method

The prime factorization method is a way to find the cube root of a perfect cube number by factoring the number into its prime components. This method is particularly useful for finding the cube root of perfect cube numbers that are difficult to estimate, such as large numbers or irrational numbers.

**Here's how the prime factorization method works:**

- Factor the perfect cube number into its prime components.
- Take the cube root of each prime component.
- Multiply the cube roots of the prime components together to find the cube root of the original number.

For example, to find the cube root of 8 (which is 2), we can factor

8 into 2*2*2 and then take the cube root of each component, which is 2. So, the Cube root of 8 is 2.

#### Related Links

- Derivative of Inverse Trigonometric functions
- Decimal Expansion Of Rational Numbers
- Cos 90 Degrees
- Factors of 48
- De Morgan’s First Law
- Counting Numbers
- Factors of 105
- Cuboid
- Cross Multiplication- Pair Of Linear Equations In Two Variables
- Factors of 100
- Factors and Multiples
- Derivatives Of A Function In Parametric Form
- Factorisation Of Algebraic Expression
- Cross Section
- Denominator
- Factoring Polynomials
- Degree of Polynomial
- Define Central Limit Theorem
- Factor Theorem
- Faces, Edges and Vertices
- Cube and Cuboid
- Dividing Fractions
- Divergence Theorem
- Divergence Theorem
- Difference Between Square and Rectangle
- Cos 0
- Factors of 8
- Factors of 72
- Convex polygon
- Factors of 6
- Factors of 63
- Factors of 54
- Converse of Pythagoras Theorem
- Conversion of Units
- Convert Decimal To Octal
- Value of Root 3
- XXXVII Roman Numerals
- Continuous Variable
- Different Forms Of The Equation Of Line
- Construction of Square
- Divergence Theorem
- Decimal Worksheets
- Cube Root 1 to 20
- Divergence Theorem
- Difference Between Simple Interest and Compound Interest
- Difference Between Relation And Function
- Cube Root Of 1728
- Decimal to Binary
- Cube Root of 216
- Difference Between Rows and Columns
- Decimal Number Comparison
- Data Management
- Factors of a Number
- Factors of 90
- Cos 360
- Factors of 96
- Distance between Two Lines
- Cube Root of 3
- Factors of 81
- Data Handling
- Convert Hexadecimal To Octal
- Factors of 68
- Factors of 49
- Factors of 45
- Continuity and Discontinuity
- Value of Pi
- Value of Pi
- Value of Pi
- Value of Pi
- 1 bigha in square feet
- Value of Pi
- Types of angles
- Total Surface Area of Hemisphere
- Total Surface Area of Cube
- Thevenin's Theorem
- 1 million in lakhs
- Volume of the Hemisphere
- Value of Sin 60
- Value of Sin 30 Degree
- Value of Sin 45 Degree
- Pythagorean Triplet
- Acute Angle
- Area Formula
- Probability Formula
- Even Numbers
- Complementary Angles
- Properties of Rectangle
- Properties of Triangle
- Co-prime numbers
- Prime Numbers from 1 to 100
- Odd Numbers
- How to Find the Percentage?
- HCF Full Form
- The Odd number from 1 to 100
- How to find HCF
- LCM and HCF
- Calculate the percentage of marks
- Factors of 15
- How Many Zeros in a Crore
- How Many Zeros are in 1 Million?
- 1 Billion is Equal to How Many Crores?
- Value of PI
- Composite Numbers
- 100 million in Crores
- Sin(2x) Formula
- The Value of cos 90°
- 1 million is equal to how many lakhs?
- Cos 60 Degrees
- 1 Million Means
- Rational Number
- a3-b3 Formula with Examples
- 1 Billion in Crores
- Rational Number
- 1 Cent to Square Feet
- Determinant of 4×4 Matrix
- Factor of 12
- Factors of 144
- Cumulative Frequency Distribution
- Factors of 150
- Determinant of a Matrix
- Factors of 17
- Bisector
- Difference Between Variance and Standard Deviation
- Factors of 20
- Cube Root of 4
- Factors of 215
- Cube Root of 64
- Cube Root of 64
- Cube Root of 64
- Factors of 23
- Cube root of 9261
- Cube root of 9261
- Determinants and Matrices
- Factors of 25
- Cube Root Table
- Factors of 28
- Factors of 4
- Factors of 32
- Differential Calculus and Approximation
- Difference between Area and Perimeter
- Difference between Area and Volume
- Cubes from 1 to 50
- Cubes from 1 to 50
- Curved Line
- Differential Equations
- Difference between Circle and Sphere
- Cylinder
- Difference between Cube and Cuboid
- Difference Between Constants And Variables
- Direct Proportion
- Data Handling Worksheets
- Factors of 415
- Direction Cosines and Direction Ratios Of A Line
- Discontinuity
- Difference Between Fraction and Rational Number
- Difference Between Line And Line Segment
- Discrete Mathematics
- Disjoint Set
- Difference Between Log and Ln
- Difference Between Mean, Median and Mode
- Difference Between Natural and whole Numbers
- Difference Between Qualitative and Quantitative Research
- Difference Between Parametric And Non-Parametric Tests
- Difference Between Permutation and Combination