Cube root of 729 by prime factorisation method
CUBE ROOT OF 729
The cube root of 729 is 9. It means that the product of 9 thrice by itself yields the number 729.
How to find the cube root?
To find the cube root of a number, we can use the prime factorisation method. By evaluating the prime factors we will make the groups of threes of the same digits and then we apply the cube root and we get the cube root of the required number. This is the easiest method to find the cube root of any number.
How to calculate the cube root of 729?
The prime factors of 729 are 3×3×3×3×3×3.
The groups of threes of the same values =
33× 33 = (3×3)3
Therefore, the cube root of 729 by prime factorization is ∛(3×3)3 = ∛93 which is equal to 9.
Illustration
Q1. a3 + 386 = 93, find the value of a.
Sol. We know that the value of 93 is equal to 729.
So, a3 + 386 = 729
a3 = 729 – 386
a3 = 343
a = ∛343
a = ∛(7×7×7)
a = ∛73
a = 7.
Thus, the value of a is equal to 7.
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Frequently Asked Questions
Q1. Is 729 both the cube as well as square?
Ans. The prime factors of 729 are 3×3×3×3×3×3, to find the square root, we will make the groups of twos of the same values. So, the groups = 32×32×32= (3×3×3)2, when we apply the square root, we get the number 27. We already know that the cube root of 729 is 9. So, 729 is the cube of 9 and the square of 27.
Q2. Is 729 a perfect cube?
Ans. When we combine the prime factors of 729 in groups of threes, we get 33 × 33 to which if we apply cube root, we get, 9. Hence, 729 is a perfect cube.
Q3. What is the cube root of 729?
Ans The cube root of 729 is equal to 9. It means that when we multiply 9 thrice by itself, it will yield the product 729.