With some basic math skills and some algebra, one can easily calculate the large cube root by following the below steps. The majority of people often depend on calculators to solve their problems. Instead of understanding concepts clearly, the over-dependence of the calculator in general stress repetition retention of pluggable formulae and techniques and also it will slaughter both your enthusiasm and capacity for mathematics. This article discusses the short trick to find out the cube root of a perfect cube in less than 5 seconds without the use of a calculator.
What is a cube and cube root?
A cube root is a special value that we will get when we multiply three times the desired number. Thus, a perfect cube is a cube of a whole number.
For example, Cube of 3 can be written as 3x3x3 = 27
and cube root of 27 = 3
Procedure for finding cube root of large numbers
To find out the cube root large number, one has to remember the cube of 1 to 10 as shown below
Number and its cube table
13 = 1
23 = 8
33 = 27
43 = 64
53 = 125
63 = 216
73 = 343
83 = 512
93 = 729
103 = 1000
Example 1: ∛50653
Let the answer format be X Y
Step 1:
To find Y, Note down the last digit in the given number
5 0 6 5 3
In this example its 3
Step 2: Now from the above table check which number cube ends in 3. In this case 73= 343. 343 is the only number which ends in 3 and it’s a perfect cube of 7. Therefore the last digit of our cube root Y = 7.
: = X_7
Step 3: In order to find X, the first digit. Consider first two digit in case of a 5 digit number.
5 0 6 5 3
For example, in this case its 50
Step 4: Compare the number 50 with the table given above. 50 is between 33 = 27 and 43 = 64
Step 5: Choose the lower value and that will be X. Therefore X = 3
Cube root of 50653 = 3 7
Example 2: ∛681472
Let the answer format be X Y
Step 1:
To find Y, Note down the last digit in the given number
6 8 1 4 7 2
In this example its 2
Step 2: Now from the above table check which number cube ends in 2. In this case 83= 512. 512 is the only number which ends in 2 and it’s a perfect cube of 8. Therefore the last digit of our cube root Y = 8.
= X_8
Step 3: In order to find X, the first digit. Consider first three digits in case of a 6 digit number.
6 8 1 4 7 2
For example, in this case its 681
Step 4: Compare the number 681 with the table given above. 681 is between 83 = 512 and 93 = 729
Step 5: Choose the lower value and that will be X. Therefore X = 8
Cube root of 681472= 8 8
Example 3: ∛328509
Let the answer format be X Y
Step 1:
To find Y, Note down the last digit in the given number
3 2 8 5 0 9
In this example its 9
Step 2: Now from the above table check which number cube ends in 9. In this case 93= 729. 729 is the only number which ends in 9 and it’s a perfect cube of 9. Therefore the last digit of our cube root Y = 9.
: = X_9
Step 3: In order to find X, the first digit. Consider first three digits in case of a 6 digit number.
3 2 8 5 0 9
For example, in this case its 328
Step 4: Compare the number 328 with the table given above. 328 is between 63 = 216 and 73 = 343
Step 5: Choose the lower value and that will be X. Therefore X = 6
Cube root of 328509 = 6 9
