Cube Root of 729
The cube root of 729, denoted as ^{3}√729, is a value which after getting multiplied by itself thrice gives the original value. This is the usual definition of the cube root of a number. Let us say, ‘n’ is the value of ^{3}√729, then n × n × n = n^{3} = 729. Since 729 is a perfect cube, we will use the prime factorisation method, to get the cube root easily. Therefore, we need to find the value of n here.
Cube root of 729, ^{3}√729 = 9 |
Also, check:
How to Find Cube Root of 729
Normally, we use prime factorisation method to find the factors of the given number, present under the cubic root. This root basically cancels the cubed number present within it.
Once we have evaluated prime factors of 729, we can pair them in a group of three which will give the cube of factors. Hence, after finding the cube of factors of the given number, we can apply the cube root, which gets cancelled with the cubes.
Let us understand it in a step by step procedure.
Step 1: Find the prime factors of 729
729 = 3 × 3 × 3 × 3 × 3 × 3
Step 2: Clearly, 729 is a perfect cube. Here we will be using laws of exponents.
729 = 3^{6} [a^{m} × a^{n} = a^{m+n}]
729 = [3^{2}]^{3} [(a^{m})^{n} = a^{mn}]
729 = 9^{3}
Step 3: Now, we will apply cube root to both the sides of the above expression to take out the factor as a single term, which is in cubes.
^{3}√729 = ^{3}√(9^{3})
So, here the cube root is cancelled by the cube of 9.
Hence, ^{3}√729 = 9
Finding the cube root of perfect cubes up to three-digit numbers is easy if we memorise the below-given table.
Number (n) |
Cubes (n^{3}) |
1 |
1 |
2 |
8 |
3 |
27 |
4 |
64 |
5 |
125 |
6 |
216 |
7 |
343 |
8 |
512 |
9 |
729 |
10 |
1000 |
But to find the cube root of four-digit numbers, we need to use the estimation method, which you can learn at BYJU’S.