Physics Wallah

Cube Root Formula: Symbol, Applications, Examples

Cube Root Formula: The cube root formula finds the cube root of a number, which, when multiplied by itself three times, equals the original number. It's symbolized as ∛.
authorImageManoj Kumar14 Sept, 2023
Share

Share

Cube Root Formula

Cube Root Formula: The cube root formula is a mathematical method used to find the cube root of a number. This cube root is the value that, when multiplied by itself three times, results in the original number. It is commonly denoted by the radical symbol ∛. This article illustrates the cube root formula with several solved examples.

Also Check - Quadrilaterals Formula

The Cube Root Formula

The formula for calculating the cube root is as follows: Cube root of x = ∛x = ∛(y × y × y) = y Where: x represents any number. y denotes the cube root of the number x. It's important to note that if y has an integer value, then the number x is a perfect cube. Also Check - Ratio and Proportion Formula

Applications of the Cube Root Formula

The cube root formula finds utility in several applications:
  • Solving cubic equations.
  • Determining the dimensions of a cube when its volume is known.
  • Providing more precise dimensions of an apartment.
Also Check - Data Handling Formula

Cube Root Formula for Negative Numbers

To compute the cube root of a negative number, the prime factorization method is employed. The process involves:
  • Finding the prime factorization of the negative number.
  • Dividing the obtained factors into three groups, each containing an equal number of each factor.
  • Multiplying the factors in any one group to derive the cube root.
  • The result will be negative, as the product of three negative values yields a negative outcome. This is represented by the negative sign accompanying the cube root of a negative number.
Also Check - Polynomials Formula

Illustrative Examples of the Cube Root Formula

Let's explore a few examples to better understand the cube root formula: Example 1: Calculating the Cube Root of 343 To find the cube root of 343: Cube root of 343 = ∛343 = ∛(7 × 7 × 7) = 7 Answer: The cube root of 343 is 7. Example 2: Determining if 512 is a Perfect Cube To ascertain whether 512 is a perfect cube or not: Cube root of 512 = ∛512 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2) = ∛(8 × 8 × 8) = 8 Answer: 512 is a perfect cube since its cube root is an integer, which is 8. Example 3: Calculating Jack Age To determine Jack age, considering that his age is the cube root of his grandmother's age (64 years): Jack grandmother's age = 64 years Jack age = Cube root of 64 = ∛64 years = 4 years Answer: Jack age is 4 years. These examples illustrate the practical application of the cube root formula in solving mathematical problems involving cube roots. Example 4: Find the Cube Root of 125 To calculate the cube root of 125: Cube root of 125 = ∛125 = ∛(5 × 5 × 5) = 5 Answer: The cube root of 125 is 5. Example 5: Determine if 1,000 is a Perfect Cube To check if 1,000 is a perfect cube: Cube root of 1,000 = ∛1,000 = ∛(10 × 10 × 10) = 10 Answer: 1,000 is a perfect cube because its cube root is an integer, which is 10. Example 6: Calculate the Cube Root of -64 To find the cube root of -64: First, determine the prime factorization of -64: -64 = (-1) × (2 × 2 × 2 × 2 × 2) = -1 × (2^5) Now, divide the factors into three groups: (-1) × (2 × 2), (-1) × (2 × 2), (-1) × 2 Multiply the factors in one group to get the cube root: (-1) × (2 × 2) = -4 So, the cube root of -64 is -4. Answer: The cube root of -64 is -4. Example 7: Calculate the Cube Root of 1 To find the cube root of 1: Cube root of 1 = ∛1 = 1 Answer: The cube root of 1 is 1. This is because any number raised to the power of 0 is equal to 1. Example 8: Determine if 27 is a Perfect Cube To determine if 27 is a perfect cube: Cube root of 27 = ∛27 = ∛(3 × 3 × 3) = 3 Answer: 27 is a perfect cube since its cube root is an integer, which is 3.

Cube Root Formula FAQs

What is the cube root formula?

The cube root formula is used to find the cube root of a number, represented as ∛x = y, where y is the number that, when multiplied by itself three times, equals x.

How do you calculate the cube root of a number?

To calculate the cube root of a number x, you find a number y such that y × y × y = x.

What are the applications of the cube root formula?

The cube root formula is used for solving cubic equations, finding cube dimensions from volume, and providing precise dimensions for various objects or spaces.

What is the procedure for computing the cube root of a negative number

To calculate the cube root of a negative number, follow the same process as for positive numbers but note that the result will be negative due to the multiplication of negative factors.

What is a perfect cube, and how can you determine if a number is one?

A perfect cube is a number that can be expressed as the cube of an integer. You can confirm if a number is a perfect cube by verifying if its cube root yields an integer value.
Popup Close ImagePopup Open Image
Talk to a counsellorHave doubts? Our support team will be happy to assist you!
Popup Image
CTA Image
008448982616
Join 15 Million students on the app today!
Point IconLive & recorded classes available at ease
Point IconDashboard for progress tracking
Point IconMillions of practice questions at your fingertips
Download ButtonDownload Button
Banner Image
Banner Image
Free Learning Resources
Know about Physics Wallah
Physics Wallah is an Indian edtech platform that provides accessible & comprehensive learning experiences to students from Class 6th to postgraduate level. We also provide extensive NCERT solutions, sample paper, NEET, JEE Mains, BITSAT previous year papers & more such resources to students. Physics Wallah also caters to over 3.5 million registered students and over 78 lakh+ Youtube subscribers with 4.8 rating on its app.
We Stand Out because
We provide students with intensive courses with India’s qualified & experienced faculties & mentors. PW strives to make the learning experience comprehensive and accessible for students of all sections of society. We believe in empowering every single student who couldn't dream of a good career in engineering and medical field earlier.
Our Key Focus Areas
Physics Wallah's main focus is to make the learning experience as economical as possible for all students. With our affordable courses like Lakshya, Udaan and Arjuna and many others, we have been able to provide a platform for lakhs of aspirants. From providing Chemistry, Maths, Physics formula to giving e-books of eminent authors like RD Sharma, RS Aggarwal and Lakhmir Singh, PW focuses on every single student's need for preparation.
What Makes Us Different
Physics Wallah strives to develop a comprehensive pedagogical structure for students, where they get a state-of-the-art learning experience with study material and resources. Apart from catering students preparing for JEE Mains and NEET, PW also provides study material for each state board like Uttar Pradesh, Bihar, and others
Privacy Policy
Terms of use
Copyright © 2025 Physicswallah Limited All rights reserved.