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251 LearnersLast updated on November 28th, 2024
Cube Root Of 189
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.
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.
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)
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.
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.
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.
Common Mistakes That Are Made While Finding Cube Root Of 189
Many kids make simple and common mistakes that will give us a wrong final answer. Let us look at some of those mistakes and stop these mistakes from happening.
Mistake 1
Thinking the Cube Root is the Same as the Square Root.
Sometimes they’d square root instead of cube root. Tell them that the cube root is to get a number that when multiplied three times (not two) with itself equals 189. That's not a square root.
Cube Root Of 189
Problem 1
Calculate 5×∛189.
5×∛189= 5×5.738= 28.69.
Explanation
First, find the cube root of 189, which is about 5.738. Then, multiply it by 5 to get 28.69.
Problem 2
Solve ∛(189+61).
∛(189+61)= ∛250= 6.299
Explanation
First, add 189 and 61 to get 250. Then, find the cube root of 250, which is close to 6.3.
Problem 3
Calculate ∛189×∛27.
∛189×∛27=∛(189×27)= ∛5103= 17.304
Explanation
When you multiply cube roots, you can find the answer by multiplying the numbers first and then finding the cube root.
Problem 4
Simplify ∛189−∛64.
∛189−∛64= 5.738−4= 1.738.
Explanation
First, find the cube roots: the cube root of 189 is about 5.738, and the cube root of 64 is 4. Then, subtract.
Problem 5
Solve ∛189−∛125.
∛189−∛125= 5.738-5= 0.738.
Explanation
First, find the cube root of 189, which is about 5.738. Then find the cube root of 125, which is 5. Subtract 5 from 5.738 to get 0.738.
FAQs For Cube Root Of 189
1.What is the approximate value of the cube root of 189?
2.Is the cube root of 189 an integer?
3.Is the cube root of 189 rational or irrational?
4.How do I express the cube root of 189 in radical form?
5.Is the cube root of 189 closer to 5 or 6?
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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