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I explain it with an example:
Find the square root of 441 in prime factorisation method:

Step I: write the prime factorisation of 441
441= 3×3×7×7
Step II: From each pair of equal factors occuring in the prime factorisation, take one of the factors and write the product of these factors. The product so obtained is the square root of the given number.
Thus, √441=√(3×3)×(7×7)

In the same way you can do the cube root.

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The first and the most important step is to memorize the cubes of 1 to 9. These would form an important part of your toolkit in solving the cube roots. Here is a table for your convenience. 1 –> 1
 2 –> 8
 3 –> 27
 4 –> 64
 5 –> 125
 6 –> 216
 7 –> 343
 8 –> 512
 9 –> 729

Once you memorize this list, the next step is to remember the last digit (unit digit) of each of these cubes.
1 –> 1
 2 –> 8
 3 –> 7
 4 –> 4
 5 –> 5
 6 –> 6
 7 –> 3
 8 –> 2
 9 –> 9 That’s it. Now that you have memorized the cubes of first 9 natural numbers and their unit digits, you are all set to amaze your friends by calculating cube roots within 5 seconds

Find out the cube root of 50653. Here is how to solve this question. The first step is to divide the number into 2 parts by separating the last 3 digits. So, we get 50  &  563 as the two parts of the number. Now, take the first part and find the largest cube contained in the first part i.e. in 50 = 27 (which is the cube of 3). The next cube i.e. 64 (cube of 4)  is larger than 50. Now, as 27 is the cube of 3, your ten’s part of cube root would be 3. [This is why we memorized the cubes] The next step is to take the last digit of the number, which in this case is 3. Which number’s cube had 3 as the unit digit? 7… right?? (7*7*7=343) Hence, 7 is the unit digit of your solution. [This is why we memorized the endings] So, your answer is 37. Try cubing 37 on a calculator to verify your answer.
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