Cube Root of 2744000

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, ∛2744000 is written as 2744000^(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 2744000, then y³ can be 2744000. Since 2744000 is a perfect cube, we can find its cube root exactly, which is 140.

Finding the cube root of a number involves identifying the number that, when multiplied three times, results in the target number. Now, we will go through the different ways to find the cube root of 2744000. 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 like 2744000, we can use the prime factorization method.

Let's find the cube root of 2744000 using the prime factorization method.

First, we factor 2744000 into its prime factors: 2744000 = 2⁶ × 5³ × 7³

Now, for every prime factor, divide the exponent by 3: (2⁶)^(1/3) = 2² = 4 (5³)^(1/3) = 5 (7³)^(1/3) = 7

Multiply these results together: 4 × 5 × 7 = 140

Therefore, the cube root of 2744000 is 140.

• 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. A perfect cube results in a whole number. For example, 2 × 2 × 2 = 8, therefore, 8 is a perfect cube.

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

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

• Rational number: A rational number is a number that can be expressed as a fraction of two integers, such as the cube root of 2744000, which is 140, a rational number.