Cube Root of 38

The cube root of 38 is a number when multiplied by itself thrice gives 38. As cube root is the inverse operation of cube, which means if ‘a’ is the cube root of b, then a³ = b.  The cube root of 38 is 3.3619. The cube root is represented by a radical sign with a 3 in the index of the root 38 . In radical form, the cube root of 38 is expressed as 338. In exponential form, the cube root of 38 is written as 38^1/3.

To find the cube root of a number, there are different methods. So children need to learn different methods to find the cube root based on the properties of numbers. For a non-perfect cube, we use Halley’s method. Some methods to find the cube root of a number are,

• Prime factorization method
• Approximation method
• Subtraction method
• Halley’s method 

As 38 is not a perfect cube, we use Halley’s method. So, let's find the value of the cube root of 38 using Halley’s method

Halley’s method is used to find the value of a non-perfect cube. The formula is 

∛a≅ x((x³+2a) / (2x³+a)) here, 

a = the number whose cube root is being calculated

x = the nearest perfect cube

Here, a = 38; x = 3

∛a ≅ 3((3³ + 2 × 38) / (2 × 3³+ 38))

∛38 ≅ 3((27 + 2 × 38) / (2 × 27 + 38))

∛38 ≅ 3.358

The value of the cube root of 38 is 3.358

• Radical symbol: Radical(√) is a symbol used to represent the square root, cube root, fourth root and higher. 

• Square root: The square root of a number is a number when multiplied by itself gives the number. For example, √4 = ±2

• Cube: The product of the number when multiplied thrice is the cube of the number. For example, 3³ = 3 × 3 × 3 = 27. 

• Exponential form: The way of expressing a number as its power. For example, 32 here 3 is the base value and 2 is the exponent.

• Index: The number written above and outside the radical symbol to represent the root. For example, for cube root - ∛ and fourth root - 4