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Cube root of 9261 is mathematically represented as ∛9261. The roots of a number is a significant concept in mathematics. It creates the basis for complex mathematical operations in trigonometry and arithmetic calculations. The root of any number when multiplied by itself by a predetermined number yields the original number. For example; the square root of 2 is 4 and the cube root of 2 is 8. This concept is also employed in physics to find velocity and acceleration. Using the cube root method, the side length of a cube can be determined if the volume is known.
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KeyTerms: Cube root, Cubic roots, Prime factors, Estimation method, Prime Factorization, Pairs of prime factors
Cube Root of 9261
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The cube root of 9261 is symbolized as ∛9261, is yielded when the original is multiplied thrice by itself.
| Cube root of 9621, ∛9261 = 21 |
The cube root of any number is the root of the cubed number. For example, if x3 = y, then ∛y = x. Thus the cube root is the inverse method of assessing a cube. This formula can be employed to find cubic roots.
Some examples of Perfect Cubes:
Cube Root of 9261
Methods to determine Cube Root of 9261
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Consider ∛9261 = x, then 9261 = x3. The value of x can be determined by using prime factorization or estimation method.
There are two ways to determine a number's cube root. As follows:
- By Estimation Method
- By Prime Factorisation Method
Cube Root of 9261 by Estimation Method
The value of ∛9261 can be evaluated using estimation method
Step 1: Take the digit from the unit’s place.
Unit place of 9261 has ⟶ 1
Step 2: Count the cube of the number 1
13 = 1
The cubic root of 9261 will have 1 at the unit place
Step 3: Now take the first number i.e, 9
9 lies between cube of 2 and 3 i.e, between 8 and 27.
So, we choose the lowest number, nearest to 9, which is 8.
Since, 23 = 8, therefore, 2 is the first digit of the desired number
Hence, ∛9261 = 21
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| Relevant Concepts | ||
|---|---|---|
| Variables and Constants | Algebra | Factors of 6 |
| Properties of LCM and HCF | Cube root table | Prime number formula |
Cube Root of 9261 by Prime Factorisation Method
Here, we'll use the prime factorization technique to identify 9261's prime factors. Then, in order to represent them as cubes, we arrange three identical prime factors into pairs. We will find the required value since the cubes of a number cancel the cube root.
Step 1: Find the prime factors of 9261
9261 = 3 x 3 x 3 x 7 x 7 x 7
Step 2: Write the factors in the form of cubes by grouping the identical ones into groups of three.
9261 = (3 x 3 x 3) x (7 x 7 x 7)
9261 = 33 x 73 [ By exponent law: am x an = am+n]
9261 = (3 x 7)3 [By exponent law: am x bm = (ab)m]
9261 = 213
Step 3: Insert the cube root on both sides of the above expression.
∛9261 =∛(213)
The cube root gets canceled by the cube of 21
Hence, ∛9261 = 21
Things to remember
- The cube root of 9261 is denoted as ∛9261.
- The ∛9261 = 21
- The cube of 9261 can be calculated by estimation method and prime factorization method
- The cube root of any number is the root of the cubed number.
- The cube root formula is x3 = y, then ∛y = x.
- The perfect cube of 2 is 8 and 3 is 27.
Sample Questions
Ques. What is cube and cube root ? (4 marks)
Ans. The most crucial ideas in various mathematical calculations are the cube and cube root. Any number's cube is the result of multiplying it by itself thrice. This result is known as the cube of any number. In other words, the integer raised to the power 3 is the cube of the original number.
The cube of a number is p x p x p or p3 if the number is "p." The opposite of a cube operation is a cube root. The number that results when a number is multiplied by itself thrice to determine its cube root is known as the cube root of that number.
Ques. Mention two types of cube root of 9261 (2 marks)
Ans. The cube root of 9261 can be determined by two ways:
- By estimation method
- By prime factorization
Ques. Define in cube root (1 mark)
Ans. The cube root of a number “x” is a number “y”, such that y 3 = x.
It implies that a number's cube root produces a value that, when cubed, yields the original number.
Ques. What is the difference between the square root and cube root? (2 marks)
Ans. A square root is a number that, when squared, yields the radicand, as opposed to a cube root, which yields the radicand when it is cubed. Additionally, the square root of a negative number cannot be negative, while the cube root of a negative number can.
Ques. Can we find the cube root for negative numbers? (1 mark)
Ans. Yes, it is possible to determine a negative number's cube root. For instance, – 4 is the cube root of – 64.
Ques. What is the original number of 9261? (1 mark)
Ans. 21 is root number of 9261
Ques. Mention the formula to find the perfect cube. (1 mark)
Ans. The cube root formula is x3 = y, then ∛y = x.
Ques. What is a perfect cube and non-perfect cube? Explain. (2 marks)
Ans. A perfect cube is a number that can be written as the result of multiplying an integer three times by itself. For example, the number 27 is a perfect cube since 3 x 3 x 3 = 27 when multiplied three times.
Any number that cannot be stated as a perfect product of multiplying an integer three times by itself is considered to be a non-perfect cube. 150, for instance, cannot be written as a perfect cube.
Ques. Find ∛343 (2 marks)
Ans. By prime factorization, 343 = 7 x 7 x 7 = 73
∛343 = 7
Ques. What is cube root of 1331 (2 marks)
Ans. By prime factorization, 1331 = 11 x 11 x 11 = 113
∛1331 = 11
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