Cube Root of 46

The Cube Root of a number is a value that, when multiplied three times by itself, gives the original number. So that means, the cube root of 46 is 3.5830. To understand it better let us convert it into an equation, consider a as the cube root of the number b, so the equation would be a³ = b.

In this case, the cube root of 46 is almost equal to 3.583, to show this like the equation as stated above: 3.583 × 3.583 × 3.583 ≈ 46. This is mostly used while studying three-dimensional shapes and the purpose of computing in many designs and learning problems.

The cube root is represented using the symbol, ∛ and the exponent used to denote it is ⅓. In exponential form, ∛46 is written as (46)^1/3. The cube root is said to be the inverse operation of cubing a number.

To find the cube root of a number, we use various methods. But to use these methods, it mainly depends on the properties of the number, like if the number is a perfect cube or not. As we are calculating the cube root for 46 we would use Halley’s method. Let us now see the methods that we use to find the cube root of 46.

1. Prime factorization method
2. Approximation method
3. Halley’s method
4. Subtraction method
    

One of the methods used to find non-perfect cubes is Halley’s method. As 46 is not a perfect cube we are using this method.

∛a≅ x((x³+2a) / (2x³+a)) here, 

a = cube root of the given number
x = the nearest perfect cube

Here, a = 46; x = 3

∛a ≅ 3 ((3³ + 2 × 46) / (2 × 3³+ 46))

∛46 ≅ 3 ((27 + 2 × 46) / (2 × 27 + 46))

∛46 ≅ 3 (119/100)

∛46 ≅ 3 ×  1.19

∛46 ≅ 3.57

The value of the cube root of 46 is 3.57
 

• Perfect cube: A perfect cube of a number is the value, when the number is multiplied three times by itself and does not have any decimal point. For example, the number 27 is a perfect cube as 3 × 3 × 3 = 27.

• Irrational Number: An irrational number is a number that cannot be written in a fraction form or has a decimal point. For example, the cube root of 46 is 3.583 which is an irrational number.

• Rounding: To round the cube root before the entire calculation might be a wrong answer. The right way is to finish the entire calculation first, then round off the value.

• Exponent form: It is a way to express a number using powers. For example, for 23 here 3 is the power and the number 2 is the base value. Therefore, the exponent is 2.

• Whole numbers:  Whole numbers are numbers that do not contain a decimal point and can be written in fraction form. For example, 1, 2, 3, 4, 5 and so on. All natural numbers are whole numbers but remember that all whole numbers are not natural numbers.