How to Use Cube Roots for Faster Maths Calculation
The cube root of a number a is that number which when multiplied by itself three times gives the number ‘a’ itself. The cube root is the inverse operation of cubing a number. The cube root symbol is ∛, it is the “radical” symbol (used for square roots) with a little three to mean cube root.
Perfect Cube Root
A cube is a number that will result in a number multiplied by itself three times for example if y is a perfect cube root of z then y = z3. If the number 5 is multiplied 3 times it results in 125 so 125 is a perfect cube root of 5.
Perfect cube root of any number = number x number x number.
A perfect cube root will always give an integer answer but a non-perfect cube root will not give an integer answer. Perfect cube root will be free from decimals and fractions.
Suppose, if n is a perfect cube for any integer m i.e., n = m3, then m is called the cube root of n and it is denoted by m = \[\sqrt[3]{n}\].
Cube root list 1 to 100 will help students to solve the cube root problem easily, accurately, and with speed.
Properties of Cube Root
The cube root of the odd number will always be an odd number.
The cube root of all even natural numbers is an even number.
The cube root of a negative number will always be negative.
the cube root will always give an integer as the answer.
Cube Root of 1 to 100
The cube root from 1 to 100 will help students to solve mathematical problems. A list of cubic roots of numbers from 1 to 100 is provided in a tabular format. The cube root has many applications in Math, especially in geometry where we find the volume of different solid shapes, measured in cubic units. It will help us to find the dimensions of solids. For example, a cube has volume ‘x’ cubic meter, then we can find the side-length of the cube by evaluating the cube root of its volume, i.e., side = \[\sqrt[3]{x}\]. Let us see the values of cubic roots of numbers from 1 to 100.
Cube Root List 1 to 100
Finding the Cube Root of a Perfect Cube
Recall that a perfect cube is a number that is the result of multiplying a number with itself 3 times.
We can think of cube roots in the same context that we view square roots. When we take the square root of a perfect square, we are searching for the number that, when multiplied by itself two times, results in the perfect square. Similarly, when we are finding the cube root of the perfect cube, we are searching for the number that when multiplied by itself three times, results in the perfect cube.
Let's solve an example.
Find \[\sqrt[3]{343}\].
Solution: To find this, we first need to break 343 into its prime factorization. To do so, we need to find the first pair of factors that include a prime number. For 343, this first pair will be 7 and 49. 7 cannot be broken down any further, but 49 can be broken into 7and 7. Therefore, we can say that \[\sqrt[3]{343}\] = \[\sqrt[3]{7}\] x 7 x 7, so we can say that the cube root of 343 is 7, where 7 x 7 x 7 = 343
Solved Examples
Example 1: Solve \[\sqrt[3]{4}\] - \[\sqrt[3]{2}\].
Solution: From the table, we can get the value of \[\sqrt[3]{4}\] and \[\sqrt[3]{2}\]
\[\sqrt[3]{4}\] = 1.587 \[\sqrt[3]{4}\] = \[\sqrt[3]{7}\]
\[\sqrt[3]{2}\] = 1.260
Therefore,
\[\sqrt[3]{4}\] + \[\sqrt[3]{2}\] = 1.587 - 1.260
= 0.327
Example 2: Evaluate the value of \[6\sqrt[3]{4}\]
Solution: We know,
\[\sqrt[3]{4}\] = 1.587
Therefore,
\[6\sqrt[3]{4}\] = 6 x 1.587
= 9.522
Quick Summary
The cube root of a number is any number multiplied three times itself.
There are two types of cube root perfect cube root and non-perfect cube root.
A perfect cube root will always give an integer answer.
A cube root can be positive as well as negative.
A cube root of a negative number will always give a negative answer.
The easiest method to solve cube root is prime factorization followed by the long division method.
Did You Know?
Any prime number p divides the cube, then p3 also divides this cube.
In the prime factorization of the perfect cube, prime numbers appear in multiples of 3.
Unit digit of a number in 0, 1, 4, 5, 6, 9 then, the unit digit of its cube also will be 0, 1, 4, 5, 6, 9.
Every non-zero number has three distinct cube roots.
The cube root is defined for all real values of X and hence cube root function passes through the origin and increases gradually.
The Cube root Function does not have any domain restrictions.
The domain and range of a cube root function are all real numbers.
Conclusion
This is the cube root list of numbers from 1 to 100. Concentrate on how the cube roots of different numbers are calculated. Focus on the features of cube roots along with examples and develop your concepts well.
FAQs on Cube Root List from 1 to 100
1. What is the definition of a cube root?
A cube root of a number is a special value that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27. The symbol for the cube root is ∛.
2. What is the main difference between a square root and a cube root?
The primary difference lies in the number of times the root is multiplied. For a square root, the value is multiplied by itself twice (e.g., √9 = 3 as 3 × 3 = 9). For a cube root, the value is multiplied three times (e.g., ∛8 = 2 as 2 × 2 × 2 = 8). Consequently, the cube root of a negative number can be a real number (∛-8 = -2), while the square root of a negative number is not.
3. How can you find the cube root of a perfect cube using prime factorisation?
To find the cube root of a perfect cube using the prime factorisation method, follow these steps:
- Step 1: Resolve the number into its prime factors.
- Step 2: Group the identical factors into sets of three.
- Step 3: Take one factor from each group of three.
- Step 4: Multiply these selected factors together to get the cube root. For example, for ∛216, the prime factors are (2 × 2 × 2) × (3 × 3 × 3). Taking one 2 and one 3 gives 2 × 3 = 6.
4. How can you tell if a number is a perfect cube just by looking at its last digit?
You cannot definitively tell if a number is a perfect cube by its last digit alone, but you can identify its potential cube root's last digit. This is a useful shortcut for checking answers. The properties are:
- If a number ends in 0, 1, 4, 5, 6, or 9, its cube root will also end in the same digit.
- If a number ends in 2, its cube root will end in 8.
- If a number ends in 8, its cube root will end in 2.
- If a number ends in 3, its cube root will end in 7.
- If a number ends in 7, its cube root will end in 3.
5. Why can a number have a negative cube root but not a negative square root?
This is because of the rules of multiplying negative numbers. When a negative number is multiplied by itself an odd number of times (like three times for a cube), the result is negative (e.g., -4 × -4 × -4 = -64). However, when a negative number is multiplied by itself an even number of times (like twice for a square), the result is always positive (e.g., -4 × -4 = +16). Therefore, no real number squared can result in a negative number.
6. How do you estimate the cube root of a number that is not a perfect cube, like 100?
To estimate the cube root of a non-perfect cube, you can find the two closest perfect cubes it lies between. For the number 100:
- We know that 4³ = 64 and 5³ = 125.
- Since 100 is between 64 and 125, its cube root must be between 4 and 5.
- As 100 is closer to 125 than to 64, we can estimate that its cube root will be closer to 5 than to 4. The actual value is approximately 4.64.
7. In what real-world situations is finding the cube root useful?
Understanding cube roots is essential in various fields. For instance:
- In geometry, if you know the volume of a cube-shaped container, you can find its side length by taking the cube root of the volume.
- In science, it is used in calculations involving volume and density, such as determining the radius of a spherical particle if its volume is known.
- In finance and economics, some complex models for calculating compound growth over three periods may involve cube roots.
