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Last updated on May 26th, 2025

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Cube Root of 8000

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We will learn the cube root concept to use it on other mathematical topics like algebra, mensuration, geometry, trigonometry, etc. So, it is as important as learning square roots. Let us now see how we can obtain the cube root value of 8000, and its examples.

Cube Root of 8000 for Omani Students
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What Is the Cube Root of 8000?

The cube root of 8000 is the value which, when multiplied by itself three times (cubed), gives the original number 8000. The cube root of 8000 is 20.  The cube root of 8000 is expressed as ∛8000 in radical form, where the “ ∛ ”  sign” is called the “radical” sign. In exponential form, it is written as (8000). If “m” is the cube root of 8000, then, m3=8000. Let us find the value of “m”.
 

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Finding the Cube Root of 8000

The cube root of 8000 can be found through various methods like:

 

 

  • Prime Factorization method

 

  • Subtraction method
     
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Cube Root of 8000 by Prime Factorization method

The steps involved to find ∛8000 are:


Step 1: Find the prime factors of 8000


After factoring 8000, make groups of three same factors out of the prime factors to get the cube root.


8000 = 2×2×2×2×2×2×5×5×5


∛8000 = ∛(2×2×2×2×2×2×5×5×5)= 2×2×5=20


After grouping together three same factors at a time, put the remaining factor under ∛.


Here, for 8000, no remaining factors are there. We get 3 groups of prime factor, i.e., (2×2×2), (2×2×2), (5×5×5)


So, 8000 is a Perfect cube. ∛8000=20.

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Common Mistakes and How to Avoid Them in the Cube Root of 8000

Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
 

Mistake 1

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For ∛8000, students can make error in the important part of prime factorization.

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 Prime Factorization is a crucial part in determining cube roots and square roots. So, use the exact prime factors and group (or pair).  
 

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Cube Root of 8000 Examples

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Problem 1

Find ((∛8000/ ∛1331) × (∛8000/ ∛1728))

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((∛8000/ ∛1331) × (∛8000/ ∛1728)) 

 


=(20/ 11)× (20 / 12)


=400/132

 

Answer: 400/132
 

Explanation

Simplified the expression and found the answer.
 

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Problem 2

The length, breadth, and height of a cuboid is 10 units, 4 units, and 5 cm respectively. To find its volume, also find the measure of a side of a cube, whose volume is 8000 cubic units.

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Volume of a cuboid = length × breadth × height = 10 × 4 × 5 cubic units = 200 cubic units.


Given, Volume of a cube = 8000 cubic units


⇒ side × side × side = 8000 cubic units


⇒ side =  ∛8000


⇒ side = 20 units


Answer: Volume of the cuboid = 200 cubic units


Side length of the cube = 20 units
 

Explanation

Applied the formula and concept of the volume of a cuboid and cube and solved.
 

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Problem 3

Multiply ∛8000 / ∛216

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 ∛8000/∛216

 

= 20/6

 

= 10/3


Answer: 10/3
 

Explanation

We know that the cubic root of 216 is 6, hence dividing ∛8000 by  ∛216.
 

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Problem 4

What is ∛(8000⁶×¹/⁶) ?

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∛(80006×1/6)

 

= (8000)1/3

 

= 20


Answer: 20 
 

Explanation

We solved and simplified the exponent part first using the fact that, (80006×1/6)=20, then solved.
 

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Problem 5

Find ∛(7000-(-1000)).

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 ∛(7000-(-1000))

 

= ∛(7000+1000)

 

=∛8000

 

=20


Answer: 20
 

Explanation

Simplified the expression, and found out the cubic root of the result. 
 

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FAQs on 8000 Cube Root

1.How many cubes are in 8000?

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2.Is 8000 a perfect square?

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3.Is 2025 a perfect cube?

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4.Why is 128 not a perfect cube?

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5.Is √8000 a polynomial?

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

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7.How can cultural or local activities in Oman support learning Algebra topics such as Cube Root of 8000?

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8.How do technology and digital tools in Oman support learning Algebra and Cube Root of 8000?

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

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Important Glossaries for Cube Root of 8000

  • Irrational Numbers - Numbers which cannot be expressed as m/n form, where m and n are integers and n not equal to 0, are called Irrational numbers.

 

  • Square root -The square root of a number is a number which when multiplied by itself produces the original number, whose square root is to be found out.

 

  • Polynomial - It is an algebraic expression made up of variables like “x” and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.

 

  • Approximation - Finding out a value which is near to the correct answer, but not perfectly correct.

 

  • Iterative method - This method is a mathematical process which uses an initial value to generate a further sequence of solutions for a problem, step-by-step. 
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About BrightChamps in Oman

At BrightChamps, we know algebra is more than digits—it’s the key to unlocking many opportunities! We’re committed to helping kids across Oman develop strong math skills, focusing today on the Cube Root of 8000 with an emphasis on understanding cube roots—in a way that’s lively, enjoyable, and simple to grasp. Whether your child is measuring the speed of a roller coaster at Oman’s Dreamland Aqua Park, tracking scores at a local football match, or managing their allowance to buy the latest gadgets, mastering algebra gives them the confidence they need for daily challenges. Our interactive lessons make learning both fun and easy. Because children in Oman learn differently, we tailor our approach to fit each child’s unique style. From the vibrant city of Muscat to the stunning natural landscapes, BrightChamps brings math to life, making it exciting throughout Oman. Let’s make cube roots an enjoyable 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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