cube root of 9261
Understand the Problem
The question is asking for the cube root of the number 9261, which is a mathematical operation involving finding a number that, when multiplied by itself three times, equals 9261.
Answer
$21$
Answer for screen readers
The cube root of 9261 is $21$.
Steps to Solve
- Identify the cube root operation
To find the cube root of the number 9261, we will use the notation $\sqrt[3]{9261}$.
- Set up the equation
Let $x$ be the cube root we are trying to find. We set up the equation:
$$ x^3 = 9261 $$
- Calculate the cube root using prime factorization
To find $x$, we can factor 9261 into its prime components.
Starting with small primes, we see:
$$ 9261 = 3 \times 3087 $$ $$ 3087 = 3 \times 1029 $$ $$ 1029 = 3 \times 343 $$ $$ 343 = 7^3 $$
So, the prime factorization of 9261 is:
$$ 9261 = 3^3 \times 7^3 $$
- Extract the cube root
Now, apply the cube root to the prime factorization:
$$ \sqrt[3]{9261} = \sqrt[3]{3^3 \times 7^3} $$
Using the property of roots, we simplify:
$$ \sqrt[3]{9261} = \sqrt[3]{3^3} \times \sqrt[3]{7^3} = 3 \times 7 = 21 $$
The cube root of 9261 is $21$.
More Information
The cube root is a specific value that represents one of the three equal factors of a number. In this case, $21 \times 21 \times 21 = 9261$. Recognizing the properties of cube roots and prime factorization can simplify finding roots of larger numbers.
Tips
- Forgetting Prime Factorization: Many might not realize they can use prime factorization for easier calculations. Always check the factors of the number, especially for larger numbers.
- Calculating Missteps: Incorrect multiplication of the base factors can lead to the wrong solution. Double-check your work.
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