Which is the most simplest and fastest way to find cube root? A shortcut
Which is the most simplest and fastest way to find cube root? A shortcut
1. 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).
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.
#2. 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.
Q. 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 474552 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.
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).
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.
#2. DERIVING CUBE ROOT FROM REMAINING DIGITSLet’s see this with the help of an example. Note that this method works only if the number given is a perfect cube.
Q. 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 474552 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.
