The cube root of 1728, expressed as 3√1728, is equal to a value that 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 the 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 methods one by one.
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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 the cube root on both 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 the four-digit number 1728 using the 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 cube 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.
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 answer.
Hence, 3√1728 = 12
Video Lesson on Finding Cube Roots
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