Shortcut Method to Find Cube Roots of Perfect Cubes
To find the cube root of perfect cubes by the shortcut method we should first know the unit value of the cube root of a number. The table given below provides the list of the corresponding unit digit according to the unit digit of the given number.\
|
Unit Digit of the number |
Unit digit of its cube root |
|---|---|
|
0 |
0 |
|
1 |
1 |
|
2 |
8 |
|
3 |
7 |
|
4 |
4 |
|
5 |
5 |
|
6 |
6 |
|
7 |
3 |
|
8 |
2 |
|
9 |
9 |
From the above table we can note that the unit digit of the cube root of a number ending with 0, 1, 4, 5, 6, and 9 remains same whereas for a number ending with 2 will have a cube root with unit digit as 8 and vica-versa and for a number ending with 3 will have a cube root with unit place as 7 and vica-versa.
Let us now understand how to find the cube root of perfect cube numbers using a shortcut and a trick.
For example, we have a number 17576
Step 1: Divide the Number
- Separate the number into groups of three.
- For 17576, the last three digits are 576, and the remaining digits are 17.
Step 2: Determine the Unit Digit of the Cube Root
- Look at the last digit of the original number. For 17576, the last digit is 6.
- Numbers with a cube ending in 6 have a cube root that also ends in 6. Therefore, the unit digit of the cube root of 17576 is 6.
Step 3: Consider the Remaining Digits
- Consider the remaining number, in this case 17.
Get the biggest perfect cube that is either less than or equal to 17. Less than 17 perfect cubes are 1 and 8. 8 is the biggest here. - The cube root of 8 is 2.
Combine the Results
- Combine the findings of the earlier results. From the cube root of 17576, the unit digit is 6 and the tens digit is 2.
- 17576’s cube root is therefore 26.
Read More,
Tricks to Find Cube Root
Finding the cube root of a large number is difficult. Simple shortcuts make the procedure faster and easier. These shortcuts use basic patterns and straightforward steps to find the cube root without complex calculations or advanced tools.
This method is useful for saving time and improving mental math skills. By learning these techniques, one can easily determine the cube root of any number.
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