313 LearnersLast updated on August 5th, 2025
Cube Root of 8000
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.
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)⅓. If “m” is the cube root of 8000, then, m3=8000. Let us find the value of “m”.
Finding the Cube Root of 8000
The cube root of 8000 can be found through various methods like:
- Prime Factorization method
- Subtraction method
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.
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
For ∛8000, students can make error in the important part of prime factorization.
Prime Factorization is a crucial part in determining cube roots and square roots. So, use the exact prime factors and group (or pair).
Mistake 2
Applying exponent rules incorrectly when finding cube roots.
∛8000 is not same as 80003. ∛8000 = 20 and 80003 is something a very large quantity.
Mistake 3
For large non-perfect cubes, students frequently estimate wrongly and leave it with a wrong result.
Keep the methods of finding cube roots in front whenever attempting large non-perfect cubes.
Mistake 4
Students typically rely on memorizing rather than understanding concepts of cube root.
Memorizing is not the solution when it comes to complex problems. So understanding the methods of finding cube roots is advisable.
Mistake 5
Misapply the cube root property like when asked to solve ∛(8000)3, students might do as ∛(8000×3)
Clear the concepts again and again if they don’t understand, where to do what. ∛(8000)3≠∛(8000×3). ∛(8000)3= 8000
Cube Root of 8000 Examples
Problem 1
Find ((∛8000/ ∛1331) × (∛8000/ ∛1728))
((∛8000/ ∛1331) × (∛8000/ ∛1728))
=(20/ 11)× (20 / 12)
=400/132
Answer: 400/132
Explanation
Simplified the expression and found the answer.
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.
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.
Problem 3
Multiply ∛8000 / ∛216
∛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.
Problem 4
What is ∛(8000⁶×¹/⁶) ?
∛(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.
Problem 5
Find ∛(7000-(-1000)).
∛(7000-(-1000))
= ∛(7000+1000)
=∛8000
=20
Answer: 20
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 8000 Cube Root
1.How many cubes are in 8000?
2.Is 8000 a perfect square?
3.Is 2025 a perfect cube?
4.Why is 128 not a perfect cube?
5.Is √8000 a polynomial?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Cube Root of 8000?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Cube Root of 8000?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
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 United Arab Emirates
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
