Cube Root of 262144

We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓.

In exponential form, ∛262144 is written as 262144^(1/3). The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 262144, then y³ can be 262144. Since 262144 is a perfect cube, its cube root is exactly 64.

Finding the cube root of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of 262144. The common methods we follow to find the cube root are given below:

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

To find the cube root of a perfect cube number like 262144, we often use the prime factorization method or direct calculation. Since 262144 is a perfect cube, we can easily find its cube root using straightforward calculations.

Let's find the cube root of 262144 using the prime factorization method.

The prime factorization of 262144 is 2^18.

We can group the factors in triples of three identical numbers: (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2)

This gives us (2³)⁶ = 64³.

Thus, the cube root of 262144 is 64.

• Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number.

• Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. For example, 4 × 4 × 4 = 64, therefore, 64 is a perfect cube.

• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 262144^(1/3), ⅓ is the exponent which denotes the cube root.

• Radical sign: The symbol that is used to represent a root is expressed as (∛).

• Rational number: A number is rational if it can be expressed as the quotient of two integers, and the cube root of a perfect cube like 262144 is rational because it is a whole number.