Cube Root of 216
The cube root of a number is a value that, when multiplied by itself three times, results in the original number. For example, if we multiply a by itself three times to get b, then b is the cube of a, or a is the cube root of b. Given that 216 is a perfect cube, we will use the prime factorization method to easily find its cube root. This page will explain the cube root of 216 in detail.
Introduction
The cube root of 216 is a number that, when multiplied by itself three times, equals 216. Let’s denote this value as ‘n’, then according to the definition of cubes, n x n x n = n^{3} = 216.
Cube Root
A number cube root is the number that, when multiplied by itself three times, yields the number 'a' itself.
For example,2^{3}=2 x 2 x 2=8 and 3^{3}=3 x 3 x 3=27
Also Read: Cube Root of 3
How to find cube root of 216
Using the prime factorization method, the following steps can be used to find the cube root of any number. This method is used to find 3216 in this case.
Step 1 : Find the prime factors of the given number ,that is 216.
From the factor tree we can observe that,
Prime factorization of 216=222333
Imp : Prime factors of a number can always be determined from the factor tree of the number.
Step 2 : 216 is a perfect cube. Group three identical factors in one group.\
216=222333
216=2333
Using the law of exponent,we get
216=63
Step 3 : Now, we will apply cube root on both the sides,
3216= 363
So, the cube root is canceled by the cube of 6
Therefore, 3216=6
Perfect cube table
Number |
Cubes |
1 |
1 |
2 |
8 |
3 |
27 |
4 |
64 |
5 |
125 |
6 |
216 |
7 |
343 |
8 |
512 |
9 |
729 |
10 |
1000 |
Simplify Algebraic Cube Root
To simplify algebraic cube roots, the following conditions must be met:
- There should be no fractional values under the radical sign.
- No ideal power factors should be under the cube root symbol.
- No exponent value should be greater than the index value when using the cube root symbol.
- If a fraction appears under the radical, the denominator should not contain any fractions.
When calculating the cube root of any integer, look for factors that appear in sets of three. For example, the cube of 27 is 3, since the factors of 27 are 3 x 3 x 3. Unlike square roots, cube roots can handle negative values under the radical sign, allowing for perfect cubes with negative values, unlike perfect squares which cannot be negative.
Use of Cubes and Cube Roots
Cubes and cube roots are widely used in various mathematical and physical operations, such as solving cubic equations and calculating the dimensions of three-dimensional objects. They are also common in everyday math computations, especially when studying exponents and determining the dimensions of a cube given its volume.
Cube Root of Negative Numbers
The prime factorization method is the most effective way to calculate the cube root of any integer, including negative numbers:
- Prime factorize the given integer.
- Group the factors into sets of three, with each set containing the same number of each component.
- Multiply the components in each group to find the cube root.
For negative numbers, simply factorize the integer and follow the same steps, noting that the cube root of a negative number will also be negative. This is represented by a negative sign preceding the cube root.
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
Frequently Asked Questions on Cube Root of 216
Ans. To find the cube root of 216, identify the number which, when multiplied by itself three times, equals 216; that number is 6.
Ans. The square root of 216 is approximately 14.696.
Ans. Using the pattern method, recognize that =6×6×6=216, so the cube root of 216 is 6.
Ans. To confirm 216 is a perfect cube, factorize it to find 216=6×6×6, indicating 6^{3} =216.