Finding the Cube root of 9261 by prime factorisation method
On multiplying a number thrice by itself, the resultant number is the cube of that number. The number that is multiplied thrice is the cube root of the resultant number. The cube root is the inverse function of the cube. The symbol of the cube root is ∛. So, in this article, we are going to find the cube root of 9261 using the prime factorisation method.
CUBE ROOT OF 9261
The cube root of 9261 is equal to 21. It means that when 21 is multiplied thrice by itself, we get the value 9261.
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 groups of threes of the same values.
After making the groups, we need to apply the cube root to those groups. We know that each group consists of three same numbers. It means that the cube is forming in every group.
When we apply the cube root, it will result in the elimination of the cube. After elimination, we select one number from each group and find their product. The resultant will give us the value of the cube root of that particular number.
How to calculate the cube root of 9261?
Now, we will perform the prime factorisation method to find the cube root of 9261.
The prime factors of 9261 are 3 × 7 × 3 × 7 × 3 × 7.
The groups of threes of the same numbers = (3×3×3) × (7×7×7) = 33 × 73 = (3 × 7)3
Thus, the cube root of 9261 by prime factorization is ∛(3 × 7)3 = ∛213 which is equal to 21.
Illustration
Q1. 8 times 9261 is equal to the cube of which number?
Sol. We know that the prime factors of 9261 are (3×3×3) × (7×7×7) = 33 × 73
The product of 9261 and 8 = 9261×8 = 8×33×73
So, when we multiply 8 by 33 × 73, the number we get is 74088.
The prime factors of 8 = (2×2×2) = 23.
So, the factors of 74088 = (2×2×2) × (3×3×3) × (7×7×7)
= 23 × 33 × 73
= (2×3×7)3
Cube root of 74088 = ∛(2×3×7)3 = 42
Therefore, 8 times 9261 is equal to the cube of 42.
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Frequently Asked Questions
Q1. Can the cube of an odd number be an even number?
Ans. No, the cube of an odd number can never be an even number. In the same way, the cube of an even number can never be an odd number.
Q2. What is the unit digit of the cube of 21?
Ans. We know that the unit digit of 21 is 1. So, 1 is multiplied thrice by itself will give us 1. Therefore, the unit digit of the cube of 21 is 1.
Q3. How many real cube roots does 9261 have?
Ans. 9261 has only one real cube root which is 21. It must be remembered that every non-zero real number has one real cube root and two complex cube roots.