Cube Root Of 1728

The cube root of a number is the value which, when multiplied by itself three times, results in the original number. In this article, we will explore ways to find the cube root of the number 1728.

Introduction

The cube root is a fundamental concept in mathematics. It plays a vital role in understanding trigonometry and arithmetic.

A root of a number is a value which, when multiplied by itself a specific number of times, equals that number.

For example, 2 is both the square root of 4 and the cube root of 8. When we multiply 2 by itself once, we get 4, so 2 squared equals 4. When we multiply 2 by itself twice more (2 x 2 x 2), we get 8, so 2 cubed equals 8.

Also Read: Cube Root of 216

Methods

There are two ways by which we can find the cube root of the number 1728.

1. Prime Factorization Method
2. Estimation Method

Prime Factorization Method

Here, we will learn how to find the cube root of the number 1728 using the Prime Factorization technique.

To calculate the cube root of 1728 using this method, we start by determining the prime factors of 1728. Once we have these prime factors, we group them into sets of three, representing the cube. This approach will give us the desired value.

Here are the steps to find the cube root of 1728:

Step 1: Find the prime factors of 1728

Prime factors are prime numbers that divide the given number without leaving a remainder. In other words, a prime factor is a number that is itself a prime number.

1728 x 2 = 864

814 x 2  = 432

432 x 2 = 216

216 x 2  = 108

108 x 2 = 54

54  x 2 = 27

27 x 3 = 9

9 x 3 = 3

3 x 3 = 1 

So multiplying the dividers we will get the output 1728. 

So we can say:

1728: 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

Step 2: Grouping the Prime Factors in the sets of threes. 

So 2’s can be grouped as (2*2*2) * (2*2*2) 

And, 3’s can be grouped as (3*3*3)

Therefore, 

1728: (2x2x2) x (2x2x2) x (3x3x3)

= 23 x 23 x 33 

Step 3: Extracting the cubic root of each side: 

Now, we will apply cubic root on both the sides:

31728 = 32 x 32 x 33

Step 4: Multiplying the cube roots to get the final answer. 

31728 = 2 x 2 x 3 

= 12

Hence, The Cubic Root of 1728 by the prime factorization technique is 12.

Also Read: Cube Root of 3

The Estimation Technique

To estimate the cube root of 1728, it's crucial to remember the cubes of integers from 1 to 10. By memorizing these values, finding the cube root of any number becomes straightforward and efficient. Here’s a table to help you memorize the cubes of the first ten integers.

Now, we will use this to get the cubic root of 1728.

Here are steps taken to get the desired output:

• Step 1: Considering the number 1728, here the unit digit is 8.
• Step 2: Now with the help of the above table, we now know that whatever will be the cubic root of the number 1728, its unit digit will be the number 2. So the cubic root of the number 1728 has number 2 at its unit place. 
• Step 3: Now, here we will consider the first digit of 1728 and ignore the remaining three numbers. So now, 728 will be ignored. With the help of the above table we know that the cubic root of the number 1 is 1. 
• Step 4: After refining the number we get the desired value as 12. So, the cube root of the number 1728 by the estimation technique is 12.