Cube Root of 1728
The cube root of 1728, expressed as ^{3}√1728, is equal to a value which when multiplied three times by itself will give the original number. To find the value of ^{3}√1728, we can use two methods, i.e. prime factorisation method and estimation method, without using any calculator. Also, learn cube root of numbers here.
Cube root of 1728, ^{3}√1728 = 12 |
Since 1728 is a four-digit number, so finding its prime factors can be a little lengthy. Thus, we can use an estimation method for fast calculation. For this method, we have to learn the value of cubes of natural numbers from 1 to 10, which is provided here in the later part. Now, let us look at both the methods one by one.
Also, check:
Cube Root of 1728 by Prime Factorisation Method
Using prime factorisation, we will find prime factors of 1728, since it is a perfect cube and then will pair them in a group of three. Let us understand it in a step by step procedure.
Step 1: Find the prime factors of 1728
1728 = 2x2x2x2x2x2x3x3x3
Step 2: Group the factors in a pair of three and write in the form of cubes.
1728 = (2x2x2)x(2x2x2)x(3x3x3)
1728 = 2^{3}x2^{3}x3^{3}
Step 3: Apply cube root both the sides and take out the terms in cubes out of the cube root.
^{3}√1728 = ^{3}√(2^{3}x2^{3}x3^{3}) = 2 x 2 x 3 = 12
Hence, ^{3}√1728 =12
Cube Root of 1728 By Estimation Method
Now, we will learn here to find the cube root of four-digit number 1728 using estimation method. Before we get to know about this method, we need to memorise the value of cubes from 1 to 10. Here is the table for reference.
Number |
Cubes |
1 |
1 |
2 |
8 |
3 |
27 |
4 |
64 |
5 |
125 |
6 |
216 |
7 |
343 |
8 |
512 |
9 |
729 |
10 |
1000 |
Now we will proceed to find the value of ^{3}√1728 following these steps:
Step 1:
We will firstly take the digit at the unit’s place.
So, here we get 8.
Step 2:
Now we will check the cubes table, the cube of which number has 8 at its unit digit place.
We see, 2^{3} = 8.
That means the cube root of 1728 will have 2 at the unit place.
Step 3:
Now ignore the last 3 digits of 1728, i.e. 728
Taking 1 as a reference number, we know the cube of 1 is equal to 1.
Therefore, we get the two-digit of the answer.
Hence, ^{3}√1728 = 12