Cube Root of 200
2026-02-28 11:03 Diff
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Last updated on August 5, 2025

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 200, and its examples.

What Is the Cube Root of 200?

The cube root of 200 is the value which, when multiplied by itself three times (cubed), gives the original number 200. The cube root of 200 is 5.84803547643.  The cube root of, 200 is expressed as ∛200 in radical form, where the “ ∛ ”  sign” is called the “radical” sign. In exponential form, it is written as (200)⅓. If “m” is the cube root of 200, then, m3=200. Let us find the value of “m”.
 

Finding the Cubic Root of 200

We can find cube roots of 200 through a method, named as, Halley’s Method. Let us see how it finds the result.
 

Cube Root of 200 By Halley’s Method

Now, what is Halley’s Method? It is an iterative method for finding cube roots of a given number N, such that, x3=N, where this method approximates the value of “x”.


Formula is ∛a≅ x((x3+2a) / (2x3+a)), where


a=given number whose cube root you are going to find


x=integer guess for the cubic root


Let us apply Halley’s method on the given number, 200.


Step 1: Let a=200. Let us take x as 5, since 53=125 is the nearest perfect cube which is less than 200.


Step 2: Apply the formula.  ∛200≅ 5((53+2×200) / (2(5)3+200)) = 5.83…


Hence, 5.83… is the approximate cubic root of 200.
 

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Common Mistakes and How to Avoid Them in the Cube Root of 200

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

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Problem 1

Find the smallest positive integer “m” such that, m × ∛216 is a perfect cube.

Okay, lets begin

 63=216


So, m×∛216= m×6


So, to make 6 a perfect cube, we need to multiply 62 with 6.


So, m=62


Answer: m=62
 

Explanation

To make 6 a perfect cube, we need to multiply 6 with 62 , so that it becomes 63. 
 

Well explained 👍

Problem 2

Simplify the expression: (∛200+∛300)(∛200²-∛(200×300)+∛300²)

Okay, lets begin

(∛200+∛300)(∛2002-∛(200×300)+∛3002)

=(∛200)3+(∛300)3    since, [ (a+b)(a2-ab+b2) = (a3+b3) ]


=200+300


=500


Answer: 500
 

Explanation

Relating with the formula for a3+b3, we simplified the given expression.
 

Well explained 👍

Problem 3

A water tank has a volume of 200 cubic meters. If water is pumped into the tank at a rate of 10 cubic meters per hour, how long will it take to fill the tank to 50% capacity?

Okay, lets begin

The target volume is 50% of 200 = 1/2 × 200 = 100 cubic meters.


Time to be taken = Volume / Rate = 100/10 =10 hours


Answer: 10 hours
 

Explanation

Time required to fill is volume of the tank divided by rate of flow of water. Using this, we solved it.
 

Well explained 👍

FAQs on 200 Cube Root

1.How do I find the cube root of 64?

The cube root of 64 can be found through an easy method known as prime factorization, where we just have to break down with prime factors of 64 to find the cube root. The exact value of cube root of 64 is 4. 

2.How do you show the prime factorization of 200?

We can express the prime factorization of 200 as 2×2×2×5×5, where 2 and 5 are the prime factors of 200.
 

3.What is 1/20th of 200?

1/20th of 200 is equal to  (1/20)×200 =10. So, 10 is the 1/20th quantity of 200.
 

4.What is the cube root of 36?

The cube root of 36 can be found through an easy method, namely, Halley’s method, by simply putting into a formula, and solving it. The approximate value is 3.301…
 

5.What are the multiples of 200?

 Multiples are the numbers when 200 is multiplied with other whole numbers. Listing out the first five multiples of 200: 200, 400, 600, 800, 1000,...

Important Glossaries for Cube Root of 200

  • Cube root properties - The features when cube root is applied to any number. Those are: 1) The cube root of all odd numbers is an odd number. The same applies for even numbers also, that is, the cube of any even number is even. 

2) The cube root of a negative number is also negative.


3) If the cube root of a number is a whole number, then that original number is said to be perfect cube

  • 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.

Fun Fact

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