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Last updated on November 28th, 2024

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Cube Root Of 189

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Mathematics has an important and interesting topic called cube root. There are many other fields that will make children use cube root. It is useful to us to find out about the volume of a cylinder, a sphere, or a cube. This is extremely critical for you to know what the cube root is. However, we’re about to go deeper into, and learn more about, the cube root and what the cube root of 189 is.

Cube Root Of 189 for Filipino Students
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What Is The Cube Root Of 189?

There are two ways a cube root of a number can be written. There are more ways to write radically, and exponentially. One radical way to express the cube root of 189 is ∛ 189 and one exponential way is (189)1/3. The cube root of the number 189 is 5.738 approximately.

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Finding The Cube Root Of 189

We have three different ways to find the cube root of a given number. All these methods are very easy to learn for a child. 

 

  • Test by prime factorization

 

  • By Halley’s Method 

 

  • Subtraction method (For Perfect Cubes)
     
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Finding Cube Root Of 189 By Prime Factorization.

Let us look at the steps that are required to get the value of cube root of 189. These steps are very to understand and will make it easy for the children to understand.

 

 

  • We will be finding the prime factors of the given number. The prime factors of 189 are 2, 3, 5. 189 has the factorization 3 × 3 × 3 × 7.

 

  • When we have found the prime factors of 189 then we will put those numbers under the cube root(∛). The cube root of 189 would be written as ∛189= ∛(3×3×3×7).

 

  • So, since there are three 3s under the cube root it will be taken out from under the cube root symbol, and it will be taken into consideration only once. Therefore, when we write it as ∛189 = 3 ∛7.

 

As we can see, 189 is not a perfect cube root. The cube root of 189, ∛189= 5.738.

Professor Greenline from BrightChamps

Cube Root Of 189 By Halley’s Method

Let us look at what Halley’s method is and how it makes it easy for us to find the cube root of a number. Let us look at how to find the cube root 189 using this method.


It is a method for finding cube roots of a given number N. If x3=N, where this method approximates the value of “x”. Formula is ∛a≅ x((x3+2a) / (2×3+a)), where a = the given number whose cube root you are going to find, x=an integer guess for the cubic root.


Let a=189. Let us take x as 5, since 53= 125 is the nearest perfect cube which is less than 189.


If we use this in the formula, ∛189≅ 5((53+2×189) / (2×53+189))= 5.738.


 So, 5.738 is the approximate cube root of 189.
 

Professor Greenline from BrightChamps

cube Root Of The 189 By The Subtraction Method

So, to find the cube root of 189 by the subtraction method, we simply must just continue to subtract by a list of prime numbers until zero. Those Prime numbers are 1, 7, 19, 37, 61, 91 and 127. However, this method only works for perfect cubes (which can hit zero exactly). However, since 189 isn't a perfect cube we can't really do this directly, and can only do close by, based on whole numbers nearby.

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Common Mistakes That Are Made While Finding Cube Root Of 189

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Cube Root Of 189

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Problem 1

Calculate 5×∛189​.

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Explanation

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Problem 2

Solve ∛(189+61)​.

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Explanation

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Problem 3

Calculate ∛189×∛27​.

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Explanation

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Problem 4

Simplify ∛189−∛64​.

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Explanation

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Problem 5

Solve ∛189−∛125​.

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Explanation

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FAQs For Cube Root Of 189

1.What is the approximate value of the cube root of 189?

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2.Is the cube root of 189 an integer?

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3.Is the cube root of 189 rational or irrational?

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4.How do I express the cube root of 189 in radical form?

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5.Is the cube root of 189 closer to 5 or 6?

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

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7.How can cultural or local activities in Philippines support learning Algebra topics such as Cube Root Of 189?

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8.How do technology and digital tools in Philippines support learning Algebra and Cube Root Of 189?

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

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Professor Greenline from BrightChamps

Important Glossaries For Cube Root Of 189

  • Cube Root (∛): The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 8 is 2, because 2×2×2=8.

 

  • Prime Factorization: Breaking down a number into its prime factors (numbers that are only divisible by 1 and themselves). For example, the prime factors of 18 are 2 and 3 (since 2×3×3=18).

 

  • Rational Number: A number that can be written as a fraction (like 1/2 or 3/4). The cube root of 189 is not rational because it cannot be written exactly as a fraction.

 

  • Irrational Number: A number that cannot be written as a simple fraction because its decimal goes on forever without repeating. The cube root of 189 is irrational because it’s a non-repeating, non-terminating decimal.
     
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About BrightChamps in Philippines

At BrightChamps, we know algebra is more than just numbers—it’s a door to countless opportunities! Our mission is to help children across the Philippines develop essential math skills, focusing today on the Cube Root Of 189 with a special emphasis on cube roots—in a way that’s lively, fun, and easy to grasp. Whether your child is calculating the speed of a roller coaster at Enchanted Kingdom, keeping score at a local basketball game, or managing their allowance to buy the newest gadgets, mastering algebra gives them the confidence they need for everyday challenges. Our interactive lessons make learning both simple and enjoyable. Recognizing that children in the Philippines learn in many different ways, we tailor our approach to fit each child’s style. From the busy streets of Manila to the beautiful islands of Palawan, BrightChamps brings math to life, making it exciting throughout the Philippines. Let’s make cube roots a fun part of every child’s math adventure!
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