To find square root or cube root of a number is not an easy task. When you’re giving a time-bound exam like CAT, CMAT, CET, NMAT, etc. this can drain you of your precious time. This is a worse deal when finding square or cube root is only part of a bigger problem, like in Data Interpretation or Compound Interest problems in Quantitative Aptitude.
So if your Mental Mathematics is a little weak, let us learn how to quickly and easily find square root or cube root of a number. This trick is sure to save you at least 40 seconds of calculations per question. At first you will find it difficult but with practice, you will be able to find square root or cube root of any number. Then let us start.
Finding Square Root:
103
2 = 10609
Step 1. Add the number to the ones digit:
103 + 3 = 106
Step 2. Square the ones digit number (if the result is a single digit put a 0 in front of it):
3
2 = 09
Step 3. Place the result from Step 2 next to the result from Step 1: 10609
97
2 = 9409
Step 1. Subtract the number from 100: 100- 97 = 3
Step 2. Subtract the number (from Step 1) from original number : 97-3 =94
Step 3. Square the result from Step 1 (if the result is a single digit put a 0 in front of it): 3
2 = 09
Step 4. Place the result from Step 3 next to the result from Step 2: 9409
48
2 = 2304
Step 1. Subtract the number from 50: 50-48=2
Step 2. Subtract the result (from Step 1) from 25: 25-2 =23
Step 3. Square the result from Step 1 if the result is a single digit put a 0 in front of it ) : 2
2 = 04
Step 4. Place the result from Step 3 next to the result from Step 2: 2304
53
2 = 2809
Step 1. Add 25 to the ones digit: 25 + 3 = 28
Step 2. Square the ones digit number ( if the result is a single digit put a 0 in front of it ) : 3
2 = 09
Step 3. Place the result from Step 2 next to the result from Step 1 : 2809
Finding Cube Root:
- REMEMBERING UNITS DIGITS
First we need to remember cubes of 1 to 10 and unit digits of these cubes. The figure below shows the unit digits of cubes (on the right) of numbers from 1 to 10 (on the left).
1 = 1
2 = 8
3 = 7
4 = 4
5 = 5
6 = 6
7 = 3
8 = 2
9 = 9
10 = 0
Now with reference to above we can definitely say that:
Whenever unit digit of a number is 9, the unit digit of the cube of that number will also be 9. Similarly, if the unit digit of a number is 9, the unit digit of the cube root of that number will also be 9. Similarly, if unit digit of a number is 2, unit digit of the cube of that number will be 8 and vice versa if unit digit of a number is 8, unit digit of the cube root of that number will be 2. Similarly, it will be applied to unit digits of other numbers as well.
- DERIVING CUBE ROOT FROM REMAINING DIGITS
Let’s see this with the help of an example. Note that this method works only if the number given is a perfect cube.
Find the cube root of 474552.
Unit digit of 474552 is 2. So we can say that unit digit of its cube root will be 8.
Now we find cube root of 447552 by deriving from remaining digits.
Let us consider the remaining digits leaving the last 3 digits. i.e. 474.
Since 474 comes in between cubes of 7 and 8.
So the ten’s digit of the cube root will definitely be 7
i.e. cube root of 474552 will be 78.
Let us take another example.
Find the cube root of 250047.
Since the unit digit of the number is 7, so unit digit in the cube root will be 3.
Now we will consider 250.
Since, 6
3 < 250 < 7
3, So tens digit will be 6
So we find cube root of the number to be 63.
