What is the cube root of 9261?
Understand the Problem
The question is asking for the cube root of 9261, which means we need to find 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
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Start with finding the cube root To find the cube root of a number, we look for a number $x$ such that $x^3 = 9261$.
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Estimate the cube root We can make an educated guess by finding two perfect cubes around 9261. For example, since $20^3 = 8000$ and $30^3 = 27000$, we know that the cube root is between 20 and 30.
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Narrow down the estimate Continuing from our estimates:
- $21^3 = 9261$
- $22^3 = 10648$
Since $21^3$ matches our target, we can confirm that this is the cube root.
- Confirm the cube root To ensure accuracy, we calculate $21^3$: $$ 21 \times 21 \times 21 = 441 \times 21 = 9261 $$
This confirms our initial work.
The cube root of 9261 is $21$.
More Information
The cube root is an important concept in algebra and helps in simplifying expressions and solving equations. Factoring and recognizing cubes can be essential in various mathematical applications.
Tips
- Not checking calculations: It’s essential to double-check your multiplication when calculating cube roots to avoid errors.
- Overestimating range: Sometimes, students might try numbers that are too far from the real cube root, leading to confusion.
