Cube Root Basics
The Cube Root of any number is another number which when multiplied by itself twice gives the number whose Cube Root is to be determined. Cube of root represented using the symbol ∛. The Cube Root of any number can also be represented in the form of an exponent as the number to the power ⅓. The Cube Root of any real number, say ‘k’, its Cube Root can either be written as ∛k or (k)⅓. We need to understand that the Cube and Cube Roots are inverse Mathematical operations. So, the Cube Root of a Cube of the number is the number itself.
How to Find a Cube Root?
The Cube Root of any real number is obtained by either the prime factorization method or estimation method when the number whose square root is to be found is a perfect Cube number. However, in most cases, it is very much recommended to memorize the Cubes and Cube Roots of the first 25 natural numbers at the least. This will help the students and the facilitators to achieve excellent scores in competitive examinations. The table below gives the Cubes and Cube Roots of the first 20 natural numbers.
Cubes and Cube Roots of the First 20 Natural Numbers
How to Find a Cube Root by the Prime Factorization Method?
In this method, the number whose Cube Root is to be found is resolved completely into its prime factors. The identical prime factors are grouped such that three identical factors form one group. To determine the Cube Root, one factor from each group is collected and multiplied together.
Step 1:
The given number is completely resolved into its prime factors. It is always recommended to start the division with the lowest possible prime number and then go to the higher prime number when the quotient is not completely divisible by the number chosen.
The given number whose Cube Root is to be determined is 74088. The prime factorization can be summarized as shown in the figure below.
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Step 2:
Write the number whose Cube Root is to be determined as the product of their primes.
The number 74088 can be written as the product of its primes as:
74088 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 7 x 7
Step 3:
Divide the factors into groups consisting of three identical factors.
74088 as the product of its primes is rewritten as:
74088 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 7 x 7
Step 4:
The Cube Root of the number is found as the product of one factor taken from each group in step 3.
So, the Cube Root of 74088 is found to be 2 x 3 x 7 = 42
How to Find the Cube Root by Estimation Method?
In the estimation method, we segregate the number into groups and then estimate its Cube Root. The steps to be followed while determining the Cube Root by estimation method are described below.
Step 1:
The given number is divided into groups of 3 digits starting from the rightmost digit of the number. If any number is left out without forming a group of three, zeros are appended to its left to make it a group of 3 digits. However, we must take care that the place value of the digit is not altered by appending zeros.
Let us try finding out the Cube Root of 74088.
So, to find the Cube Root of 74088, we should divide the number into groups of three digits starting from the digit in the unit’s place.
074 088
Step 2:
From the first group starting from the right, note down the unit’s digit.
The first rightmost group in step 1 is 088 and the digit in its unit’s place is 8.
Step 3:
Estimate the digit in the unit’s place of the Cube Root of the given number using the lookup table given below.
The digit in the unit’s place obtained in step 1 is ‘8’ and hence the unit’s digit of the Cube Root of 74088 is also ‘2’.
Step 4:
Now, consider the second group from the right. Check the perfect Cube numbers between which this number lies. Suppose the number in this group lies between A3 and B3 and is closer to B3, then the ten’s digit of its Cube Root is considered as B.
In the given number 74088, the second group of 3 digits from the right is 074.
This number lies between two perfect Cube numbers 64 and 125 i.e. 43 and 53. Because 74 is closer to 64 i.e. 43, the ten’s digit of the Cube Root of 74088 is 4.
The Cube Root of 74088 found using the estimation method is 42.
Fun Facts
Cube and Cube Root are inverse operations and hence the Cube Root of the Cube of a number is the number itself.
The Cube Root of a perfect Cube number is always a whole number.
Prime factorization and estimation methods can be used to find the Cube Roots of Perfect Cubes only. To determine the Cube Roots of nonperfect Cubes, there are a few tricks that can be followed.
FAQs on How to Find Cube Root?
1. What is Cube and Cube Root?
Cube and cube root are the most important concepts in various mathematical calculations. A Cube of any number is that number which we get when we multiply the number whose cube is to be determined by itself twice. In other words, the cube of a number is the number raised to the power 3. If the number is ‘p’, then its cube is p x p x p or p3. Cube root is the inverse operation of a cube. The Cube root of a number is that number which when multiplied by itself twice gives the number whose cube root is to be determined as the answer.
2. Where Do We Use Cubes and Cube Roots?
Cubes and cube roots are used in several Mathematical and Physical computations. It is quite often used to derive the solutions of cubic equations. To be more specific, the knowledge of cube roots can be used to determine the dimensions of three dimensional objects with specific value. Cubes and cube roots are also used in day to day calculations of Mathematics while learning the concepts such as exponents.
3. What is a Cube Root?
The Cube Root of any number is another number which when multiplied by itself twice gives the number whose Cube Root is to be determined. Cube of root represented using the symbol ∛. The Cube Root of any number can also be represented in the form of an exponent as the number to the power ⅓. The Cube Root of any real number, say ‘k’, its Cube Root can either be written as ∛k or (k)⅓. We need to understand that the Cube and Cube Roots are inverse Mathematical operations. So, the Cube Root of a Cube of the number is the number itself.
4. How to find the Cube Root?
The Cube Root of any real number is obtained by either the prime factorization method or estimation method when the number whose square root is to be found is a perfect Cube number. However, in most cases, it is very much recommended to memorize the Cubes and Cube Roots of the first 25 natural numbers at the least. This will help the students and the facilitators to achieve excellent scores in competitive examinations.
5. Where can I find notes on finding the Cube Root of a number?
Mathematics is everywhere around us but starts basically from numbers. It has a lot in depth which is slowly taught at higher levels of education. Particularly, this chapter is all about multiplication and division where students might make silly mistakes. Don't worry because, at Vedantu, we provide solutions to various chapters to students as it is essential for one to have good practice before the main exam. Also, you can get them in PDF format with expert answers at our app or website.
6. Is Mathematics tough?
Mathematics is a subject that has 10-12 chapters that mainly cover the basics of algebra, geometry, linear equations, and so on. Students find it a little difficult due to the variation from primary education to secondary. Also, students have posed essay questions in a slightly twisted way to enhance their mental ability. Hence, initially, students might face problems with Mathematics but remember that it is the foundation to all the higher levels of education one may pursue. Timely revisions would be of great help.
7. How to revise Mathematics?
Mathematics isn’t a subject that can be memorized, whereas it is one such subject that requires conceptual understanding to solve problems and score well in exams. Solving different types of problems in the same concept would benefit students at a later date. Practice daily and for detailed notes, keywords that’ll be handy, students can join us at the Vedantu app for a live doubt clarification session.