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.
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 = 23x23x33
Step 3: Apply cube root both the sides and take out the terms in cubes out of the cube root.
3√1728 = 3√(23x23x33) = 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.
Now we will proceed to find the value of 3√1728 following these steps:
We will firstly take the digit at the unit’s place.
So, here we get 8.
Now we will check the cubes table, the cube of which number has 8 at its unit digit place.
We see, 23 = 8.
That means the cube root of 1728 will have 2 at the unit place.
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