What is the cube root of 4913?
Understand the Problem
The question is asking for the cube root of the number 4913. To find this, we will calculate a number that when multiplied by itself three times yields 4913.
Answer
$17$
Answer for screen readers
The cube root of 4913 is $17$.
Steps to Solve
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Identify the operation needed We need to find the cube root of 4913, which can be expressed as $x = \sqrt[3]{4913}$.
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Estimate the cube root We start by estimating the cube root by determining which two integers $n$ and $n+1$ would satisfy $n^3 < 4913 < (n+1)^3$.
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Calculate cubes of integers Calculating some cubes to find bounds:
- $17^3 = 4913$
- $16^3 = 4096$
- $18^3 = 5832$
- Confirm the result Since $17^3 = 4913$, we confirm that $x = 17$. Therefore, $\sqrt[3]{4913} = 17$.
The cube root of 4913 is $17$.
More Information
The number 4913 is a perfect cube, as it can be expressed as $17^3$. This property makes it easier to find the cube root since it is a nice whole number.
Tips
- Miscalculating the cubes of integers could lead to an incorrect estimate of the cube root. Always double-check calculations for accuracy.
- Skipping the estimation step might lead to confusion about the range of values for the cube root.
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