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Last updated on November 30th, 2024

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Cube root of 1

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The cube root of a number is a number multiplied by itself thrice equals the original number. We apply cube roots in geometry for calculating volumes, to scale objects in physics and in engineering to measure density and many others. Let's learn more about the cube root of 1.

Cube root of 1 for Indian Students
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What is the cube root of 1?

∛1 — is the symbolic representation of ‘cube root of 1’. 


∛1=1 


∛1 has three roots→ 1,𝛚, 𝛚2, which on multiplication together gives “1” as a product. 1×𝛚×𝛚2=1.

 

As mentioned above, the cube root of 1 or the cube root of unity are 1,𝛚, 𝛚2, where 1 is a real root, 𝛚 and 𝛚2 are the imaginary roots.


The essential features or properties of the cube root of 1 are: 


The imaginary roots 𝛚 and 𝛚2 when multiplied together, yields 1


    𝛚×𝛚2= 𝛚3=1


The summation of the roots is zero → 1+𝛚+𝛚2=0.


The imaginary root 𝛚, when squared, is expressed as 𝛚2, which is equal to another imaginary root.
 

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Finding the Cube Root of 1

Now, let us find the meaning of 𝛚 here. To find the cube root of 1, we will make use of some algebraic formulas. We know that, the cube root of 1 is represented as ∛1. Let us assume that ∛1= a, so,


∛1= a


⇒ 1 = a3


⇒ a3- 1 = 0 


 ⇒ (a - 1)(a2+a+1) = 0              [using a3-b3= (a - b)(a2+a.b+b2)]


⇒ a - 1 =0


⇒ a= 1  …………..(1)


Again, a2+a+1 = 0


⇒ a = (-1 ±√(12–4×1×1)) / 2×1


⇒ a =  (-1 ±√(–3)) / 2


⇒ a =  (-1 ± i√3) / 2


⇒ a =   (-1 + i√3) / 2     …………(2)


Or


a =  (-1 - i√3) / 2        …………(3)


From equation (1), (2), and (3), we get,


The roots are →  1,  (-1 + i√3) / 2 and  (-1 - i√3) / 2
 

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Common Mistakes and How to Avoid Them in the Cube Root of 1

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Cube root of 1 examples

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Problem 1

Solve — ∛8×1

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Explanation

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Problem 2

The volume of a cube is 1 cubic unit. Find the length of the side.

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Explanation

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Problem 3

Find z where z³-1 = 0

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Explanation

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FAQs on the cube root of 1

1.What is the cube of (-1)?

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2.Is the cube root of 1 an imaginary number?

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3.What is the square of negative 1?

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4.Is √1 real?

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5.Why is i²= -1?

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6.How does learning Algebra help students in India make better decisions in daily life?

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7.How can cultural or local activities in India support learning Algebra topics such as Cube root of 1 ?

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8.How do technology and digital tools in India support learning Algebra and Cube root of 1 ?

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9.Does learning Algebra support future career opportunities for students in India?

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Important Glossaries for Cube root of 1

  • Natural numbers — Numbers that range from 1 to infinity. 

 

  • Whole numbers — The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity. 

 

  • Integers — Integers can be a positive natural number, negative of a positive number, or zero. We can perform all the arithmetic operations on integers. The examples of integers are, 1, 2, 5,8, -8, -12, etc.

 

  • Square root  — The square root of a number is a value “y” such that when “y” is multiplied by itself → y × y, the result is the original number. 
     
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About BrightChamps in India

At BrightChamps, we understand algebra goes beyond symbols—it’s a pathway to limitless opportunities! Our mission is to help children throughout India master vital math skills, with today’s focus on the Cube root of 1 and a special emphasis on grasping cube roots—in a way that’s engaging, enjoyable, and easy to follow. Whether your child is calculating the speed of a passing train, keeping track of scores during a cricket match, or managing pocket money for the latest gadgets, mastering algebra builds the confidence needed for everyday life. Our interactive lessons ensure learning is simple and fun. Aware that children in India learn in various ways, we tailor our teaching to each child’s unique style. From the busy markets of Mumbai to the vibrant streets of Delhi, BrightChamps makes math relatable and exciting all over India. Let’s make cube roots a fun part of every child’s math journey!
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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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