Cube Root Of Perfect Cubes - The Vedic Mathematics Way

I. Introduction

In this chapter we will look at the method to find the cube roots of numbers that are perfect cubes, that is, numbers whose cube roots are integers.

II. Method

To use this method you will need to remember the cube roots of single digit integers, that is $1$ to $9$.

	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$
Cube	$0$	$1$	$8$	$27$	$64$	$125$	$216$	$343$	$512$	$729$
Last Digit	$0$	$1$	$8$	$7$	$4$	$5$	$6$	$3$	$2$	$9$

Observe, that each of the single digits have a unique last digit for its cube. Also observe, that the cube root of any $3$-digit number is a single digit.

Four digit numbers will have a $2$ digit cube root, because the smallest $4$-digit number, $1000$ has a cube root of $10$.

The method here is very simple. Given any number, $4$ to $6$ digits long, we follow the given steps to find the cube root.

$Step\ 1:$ Consider the unit's digits of the given number.

$Step\ 2:$ If the given number is a perfect cube, we will know the unit's digit of the cube root from this digit.

$Step\ 3:$ Eliminate the rightmost $3$ digits of the given number and take the rest.

$Step\ 4:$ Find the largest perfect cube, not greater than this remaining number, find its cube root.

$Step\ 5:$ Append the unit's digit of the cube root to this cube root to get your final answer.

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III. Examples

Let us see a couple of examples in this section.

$\underline{Example\ 1:}$

Let us start by finding the cube root of $389017$

- The last digit of the given number number is $7$. Therefore, the last digit of the cube root is $3$.

- Remove the last $3$ digits and take the rest, $389$$\cancel{017}$ to get $389$

- Find the largest perfect cube not exceeding $389$, which is $343$.

- The cube root of $343$ is $7$.

- Placing $7$ in front of the unit's digit $3$ we get the cube root as $73$

$\underline{Example\ 2:}$

We will apply this method to find the cube root of $140608$

- The given number ends with $8$, therefore the unit's digit of the cube root is $2$.

- We remove the last $3$ digits and are left with $140$

- The largest perfect cube not exceeding $140$ is $125$.

- The cube root of $125$ is $5$.

- Placing $5$ in front of the unit's digit $2$ we get $52$.

- Therefore, $\sqrt[3]{140608} = 52$

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IV. Practice Time

Use the following widget to practice calculation of cube roots. The problems will contain perfect cubes only. Use the method described in $Section\ II$ of this booklet to find the cube roots.

Finding Squares -