Cube Root of 117649

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, ∛117649 is written as 117649^(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 117649, then y³ can be 117649. Since 117649 is a perfect cube, its cube root is exactly 49.

Finding the cube root of a number involves identifying the number that, when multiplied three times by itself, results in the target number. Now, we will go through the different ways to find the cube root of 117649. The common methods we follow to find the cube root are given below:

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

Since 117649 is a perfect cube, we can use the prime factorization method efficiently.

Let's find the cube root of 117649 using the prime factorization method.

First, factorize 117649:

117649 = 7 × 7 × 7 × 7 × 7 × 7 = 7⁶

Since 7^6 can be written as (7³)², the cube root of 117649 is 7², which equals 49.

Finding the perfect cube of a number without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:

Children often try to calculate an exact whole number for the cube root of numbers that are not perfect cubes.

For example, they assume that they would get an exact whole number for numbers like 39. To avoid this error, memorize that some numbers don't have a perfect cube root. However, 117649 is a perfect cube, and its cube root is exactly 49.

Most of us might forget the fact that cube root can also be written in exponent form.

For example, forgetting that the cube root of 117649 can be expressed as 117649^(1/3). To avoid this error, always learn the forms in which we can express the cube root of a number. plain_heading7 Using incorrect methods for perfect cubes plain_body7 Instead of using prime factorization for perfect cubes, children might end up using approximation methods. For example, they might try to find the cube root of 117649 using iterative methods. Remember that for perfect cubes, prime factorization is the most efficient method.

• 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 always results in a whole number. For example: 7 × 7 × 7 = 343, therefore, 343 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 which denotes the cube root of a.
   
• Radical sign: The symbol that is used to represent a root, which is expressed as (∛).
   
• Rational number: Numbers that can be expressed as a ratio of two integers. The cube root of 117649 is rational because it is a whole number.