Calculate Cube Roots - CSAT Preparation - UPSC

Introduction

• We have heard many people saying that there is actually no shortcut to find the cube root of a number. This is not true. In fact, there are ways to quickly, easily and accurately calculate the cube root of a given number. 
• These ways when mastered can help you to get the cube root of a number in less than 5 seconds. 
• We are now going to have a look at the simplest & fastest way of calculating the cube root of a number in this article.

Calculating the Cube Root of a number quickly and accurately

• 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. Here is the list again, only with unit digits this time.
  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 (given that they have not read this article).

Let us see how to calculate cube roots in less than 5 seconds.
Q.1. 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.

Let us solve another example to show how the answer can be achieved in less than 5 seconds.

Q.2. Calculate the cube root of 941192.
By Step 1: We get two parts i.e. 941 and 192.
By Step 2: The largest cube less than 941 is 729 (cube of 9). So, ten’s digit is 9.
By Step 3: The ending digit is 2. Hence, unit’s digit is 8. That’s it. 98 is the answer.
Practice it a bit and you would be able to solve this in even less than 5 seconds.