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Last updated on November 28th, 2024
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.
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.
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.
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.
As we can see, 189 is not a perfect cube root. The cube root of 189, ∛189= 5.738.
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.
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.