What is Cube Root?
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 1 to 100
1. What is Cube and Cube Root ?
Definition of Cube
If a number is multiple three times with itself, then the result of this multiplication is called the cube of that number. Example: cube of 6 = 6 × 6 × 6 = 216.
Definition of Cube Root
The cube root is that number which on cubing itself gives the given number. The cube root is denoted by the symbol ‘ ∛ ’. Example, \[\sqrt[3]{8}\] =\[\sqrt[3]{2}\] × 2 × 2 = 2
2. How to calculate Cube Root of a number by Prime Factorisation Method?
Prime Factorisation Method
This method has the following steps
Step 1: Find the product of prime factors of the given number.
Step 2: Keep these factors in a group of three.
Step 3: Take the product of these prime factors picking one out of every group ( group of three) of the same primes. The product of these numbers gives us the cube root of a given number.
Ex. Find the cube root of 9261.
(A) 22
(B) 21
(C) 23
(D) 24
Solution
3 | 9261 |
3 | 3087 |
3 | 1029 |
7 | 343 |
7 | 49 |
7 | 7 |
1 |
Prime factors of 9261
= (3×3×3)×(7×7×7)
Now, taking one number from each group of three, and evaluating it we get
= 3 x 7
\[\sqrt[3]{9261}\] = 21
3. What is the difference between cube root and square root?
Cube root is the number that produces a given number when multiplied three times. Whereas, a square root is a number that produces a number when multiplied by itself. It means the cube root is obtained when any number is multiplied by 3 and the square root is obtained when any number is multiplied twice. The prime difference between the cube root and the square root is the multiplication factor. A square root cannot be negative but a cube root can be negative. Negative square roots give imaginary numbers but negative cube roots only give real numbers.
4. Can cube root be negative?
Unlike a square root, the result of a cube root can be any real number: positive, negative, or zero. Also, the difference from a square root is the domain restriction on the radicand. the radicand of a cube root can be negative while still achieving a real result for the cube root.
5. What are the methods to solve cube root?
There are two methods to solve any cube root of the given number. For perfect cube roots, prime factorization can be used but for non-perfect cube roots, the division method can be used. In the prime factorization method, the number specified is written as the multiplication of its prime factors. Cube roots can be of two types: perfect cube root and non-perfect cube root.