Math Tricks - How to find the Cube Root of numbers without calculator

CUBE ROOT

In this post i will explain top methods and tricks to find cube root of numbers easily without calculator in mind. Cube root of any number is a quantity which when multiplied by twice of itself gives the same number. For example: '3' is a cube root of '27' which when multiplied by itself twice produces the number '27'.

Finding the Cube Root of Perfect Cube

• Check the unit digit of the given number and write those numbers whose cubes give the same unit digit.

• Now neglect last three digits of the given number and find the number whose cube is nearest to the given number but not greater.

To find cube root up-to six digit numbers, we need to remember the cubes up-to 10.
(1)3 = 1
(2)3 = 8
(3)3 = 27
(4)3 = 64
(5)3 = 125
(6)3 = 216
(7)3 = 343
(8)3 = 512
(9)3 = 729
(10)3 = 1000


Example: Find the cube root of 19683?
Solution:

 Here unit digit is '3', that number whose cube gives the same unit digit is '7'.

After omitting last three digits which are “683”, only “19” remains, now write those numbers whose cube is nearest to 19, but not greater, and that is “2”.

So answer is '27'.

Cube Root using Factorization Method

 Step 1:  Write the factors of given number.

 Step 2:  Make pairs of numbers repeated thrice.

 Step 3:  Write each number repeated thrice and multiply these numbers.

 Step 4:  Left those numbers which are repeated less then 3 times inside cube root.

Example: Find the cube root of 2160? 
Solution:

 

Cube Root Of Non-perfect Cubes

Example: Find the cube root of 4.
Solution:  Step 1:  First make a guess 'x' as the cube root of number 'n'
Here number is '4', so i am guessing '2' as a cube root of 4.

 Step 2:  Divide the number by 'x' and divide this quotient by 'x' again.
⇒ 4/2 = 2 and 2/2 = 1

 Step 3:  Take the average of 'x', 'x' and final quotient.
⇒ (2 + 2 + 1)/3 = 1.67

It is closer cube root than the initial guess, but for better accuracy repeat the above steps.
⇒ 4/1.6 = 2.5 and 2.5/1.6 = 1.562
Average = (1.6 + 1.6 + 1.562)/3 = 1.5873

So cube root of 4 is 1.5873 approx.


 Direct Formula: 

Here N = given number
x = guess of approximate square root
n = index of root, For square root it will be 2 and for cube root it will be 3

Now for Cube root of 4: N = 4; x = 2; n = 3
⇒ (2 x 2 + 4/22)/3 = 5/3 = 1.67

This is first approximate value, for better accuracy repeat the above step with x = 5/3 or 1.67
⇒ [2 x 1.67 + 4/(1.67)2]/3 = 1.591

So cube root of 4 is 1.591 approx. We can repeat steps further for accuracy up-to 6 decimal places.


These are few tricks for calculating cube root of any number quickly without calculator. In examination if all the given options are natural numbers then First method of finding cube root will save a lot of time. But if any option says 'none of these' or options are in decimals, in that case first method may or may not give accurate result because that method is to find the cube root of perfect cubes. So better to practice all the methods of finding cube root. Good Luck 👍