Cube Root of 125

The cube root of 125 is 5. The cube root of 125 is expressed as ∛125 in radical form, where the “∛"  sign is called the “radical” sign. In exponential form, it is written as (125^)⅓
 

We can find the cube root of 125 through various methods. 

• Prime Factorization method

• Subtraction method 
   

Finding a cube root of 125 through the Prime Factorization method involves determining the factor of 125.

Step 1: Find the prime factors of 125.

So, 125 = 5x5x5 

Step 2: Group the factors of 125 in a group of 3.

Step 3: Since 125 is a perfect cube, we have a pair of 3, so there is no need to expand it further.

The cube root of 125 can be written as ∛125 = ∛5x5x5 = 5 

Therefore, the cube root of 125 is 5. 
 

In this method, from the given cube number, 1, 7, 19, 37, 61, 91, 127, 169... are successively subtracted till we get zero. The number of times subtraction was performed gives the cube root of the given number. 

Step 1: Subtract the 1st odd number : 125 - 1 = 124 

Step 2: Subtract the next odd number: 124 - 7 = 117

Step 3: Subtract the next odd number: 117 - 19 =  98

Step 4: Subtract the next odd number: 98 - 37 = 61 

Step 5: Subtract the next odd number: 61 - 61 = 0

Here the subtraction took place five times to reach zero.

Hence the cube root of 125 is 5. 

We get a cube root of a number when multiplied by itself three times. Methods like Prime Factorization, and subtraction methods are useful in finding the cube root of a perfect cube. Since we have found the cube root of 125 using all these methods, it has become quite simple to find the cube roots of any other number. 
 

• Perfect cube: Perfect cube is the number that can be expressed as the cube of an integer. 

As 125 = 5x5x5, it is a perfect cube 

• Radical form:It’s the notation used to represent roots, ∛125

• Exponent form:It’s the notation used to represent roots using exponents, (125)⅓

• Equation:It is a mathematical expression that asserts the quality of two expressions.