Cube Root from 1 to 100

The cube root of 1 to 100 is a number that multiplies itself three consecutive times to give the original number. The calculation of these roots is valid for both positive and negative values. The value that lie from 1 to 100 is approximately 4.64158. Numbers 1, 8, 27, and 64 are the perfect cubes between these, which means their cube roots are whole numbers, while the others are non-perfect cubes because they have irrational cube roots.

The cube written in the radical form as ∛x and in exponential form as x^1/3, where x is a value between 1 and 100. Students can solve such problems more easily if they know this.

Cube roots from 1 to 100 helps students to see the number that, when to be multiplied by itself 3 times, will give the original number. The students would find it easier, faster, and would learn quicker if they knew these cube roots when it comes to solving math problems.
 

Learning the cube roots of numbers from 1 to 100 can be easier and faster. With the cube root of these number, a student can solve problems a lot faster. Here is the complete list of cube roots from 1 to 100.
 

Cube Roots from 1 to 10

The cube roots of numbers from 1 to 10 are simple to get and they may be both whole and decimal values. These are the numbers which, when you multiply by themselves three times, will give you the original value.

Cube Root from 11 to 20
As for numbers from 11 and 20, the cube roots become much more complicated but can still easily be calculated with a calculator.
 

Cube Roots from 21 to 30
The cube root of a number between 21 and 30 is slightly larger, and most of them are decimal values. To understand these cube roots, students can use the third root of a cube to complete problems.

Cube Root from 31 to 40
The cube roots of numbers from 31 to 40 just get larger and larger with increasing numbers. These values are useful for solving math problems.
 

Cube Roots from 41 to 50
 The cube roots of numbers between 41 and 50 are useful in advanced calculation, especially in science. The problem of cube differences is greatly simplified by a deep understanding of cube formulas.
 
Cube Roots from 51 to 60
The cube roots of 51 to 60 numbers are going up, which means they are mostly decimal. When you understand them, it is easy to solve any cube related problem. 

Cube Roots from 61 to 70
The cube roots become little larger when we go from 61 to 70, but they are still not hard to calculate. The cube roots of these numbers are very useful in such fields as physics and engineering.

Cube Roots from 71 to 80
The cube roots of numbers between 71 and 80 are not yet remain simple to calculate. These numbers are helpful in solving difficult problems using the concept of cubes in algebra.

Cube Roots from 81 to 90
The cube roots of integers starting from 81 and ending at 90 keep on increasing, and most of them are non-perfect cubes. With the help of these roots we can solve problems with cubes which are easy to solve.

Cube Roots from 91 to 100
Numbers from 91 to 100 have cube roots that give the highest values, with cube roots around 4.64. These cube roots are crucial when handling higher-order math problems.
 

The perfect cube roots from 1 to 100 are 1, 2, 3, and 4, whereas their corresponding perfect cubes take values 1, 8, 27, and 64. A perfect cube is a number that arises from multiplication of number by itself three times, such as 4 x 4 x 4 = 64, which is perfect cube of 64.

Non-perfect cube roots from 1 to 100 are the numbers which when multiplied by themselves three times do not give whole number. They cannot be found in the series of numbers which when multiplied by themselves 3 times will produce the decimal value.
 

When calculating cube roots from 1 to 100, use prime factorization by grouping three prime factors. You can also estimate by finding the nearest perfect cubes.
 

In this method,

• Divide the given number into all its prime factors

For example, the prime factorization of 27 is 3 x 3 x 3

• Combine identical factors in sets of three

For example, (3 x 3 x 3) is one group

• Pick one factor from each group and multiply them.

For example, for 27: the cube root is 3.
 

• Find the two nearest perfect cubes.For example, for 30, the closest are 27 (3³) and 64 (4³)

• Determine where the number lies between them and make a guess. For example, 30 is closer to 27, so the cube root is slightly above 3, around 3.1 or 3.2

• Check your estimate by cubing. For example, 3.13 = 29.79, which is close to 30, so 3.1 is a good estimate

Different methods are used to find the cube roots, depending on whether the number is perfect cube or not. The rules to find cube root of a number from 1 to 100 are as below. 

Rule 1: Exact Cubes

To obtain the cube root of exact cube, first factorize it into prime factors and arrange them in groups of three. For example, 27= 3 x 3 x 3, so the cube root is 3.

Rule 2: Approximation for Non-Exact Cubes

To estimate the cube root of a given number, one way to find the nearest perfect cubes and adjust the value. Using 30 as an example, the closest perfect cubes are 27 (3³) and 64 (4³), from which we understand that the cube root is about 3.1.

Rule 3: Properties of Cube Roots

Use cube root properties, such as ∛(a.b) = ∛a . ∛b, to make the calculation less difficult. With this rule you can factor out the separate cube roots of a product. For example, ∛(8.27) = ∛8 x ∛27 = 2 x 3 = 6 

Rule 4: Using Cube Root Formula

To calculate the cube root directly, use the formula x = ∛y, where y is the value you desire to find the cube root of a number. For example, if y = 64, x = ∛64 = 4. With this formula, you can quickly determine the cube root of any number.

Below are some helpful tips and tricks for students given how to compute cube roots from 1 to 100 more quickly:

• Keep in mind the cube roots of perfect cubes, such as 1, 8, 27, and 64. Which will speed up the calculation.
   
• For identifying the cube root of non-perfect cubes by the closest perfect cubes and adjust your guess accordingly to make the best estimate. 
   
• Divide the numbers into their prime factors and combine them in sets of three to make finding the cube root easier.
   

Rational number: The rational number is the number which is a quotient of two integer q and p. Where p and q are integers, and q≠0. For example, 2/1

Exact cube: An exact cube is also a perfect cube. A number which can be written as a product of an integer multiplied by itself three times. For example, 8 = 2 x 2 x 2. So 8 is a perfect cube.

Non-perfect cube: A number that cannot be described as cube of an integer. For example, 12 which is a non-perfect cube because there is no whole number whose cube i equals 12.