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.

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)
   

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.

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׳+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.

• 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.