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Last updated on November 30th, 2024

Cube Root of 8000

Q: How many cubes are in 8000?

By prime factorization, we can find out how many cubes 8000 consists of. 8000 = 2×2×2×2×2×2×5×5×5. So, it contains two pairs of 8, which is a cube of 2, and also 125, which is a cube of 5. Also, 2×2=4, and there are three 4s, where 43=64 So, total four cubes inside 8000.

Q: Is 8000 a perfect square?

8000 is not a perfect square, since the square root value of 8000 is 89.442…, which is neither a whole number nor a rational number.

Q: Is 2025 a perfect cube?

We can check this by prime factorization of 2025. 2025=3×3×3×3×5×5. So, observe that 3 cannot group in the power of three. Hence, 2025 is not a perfect cube.

Q: Why is 128 not a perfect cube?

We can check this by prime factorization of 128. 128=2×2×2×2×2×2×2. So, observe that, we can make 2 groups of 2s in a power of three, but a single 2 is remaining. Hence, 128 is not a perfect cube.

Q: Is √8000 a polynomial?

√8000 is not a polynomial, since it is a constant number, and not a variable. It does not involve any variables raised to whole number exponents.

Professor Greenline Explaining Math Concepts

Foundation

Intermediate

Advance Topics

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

Cube Root of 8000 Examples

Ray, the Character from BrightChamps Explaining Math Concepts

Problem 1

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

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Explanation

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.

Explanation

Problem 3

Multiply ∛8000 / ∛216

Explanation

Problem 4

What is ∛(8000⁶×¹/⁶) ?

Explanation

Problem 5

Find ∛(7000-(-1000)).

Explanation

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?

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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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.