What is the cube root of 10000?
Understand the Problem
The question is asking for the cube root of 10000, which is a mathematical calculation. To find the cube root, we need to determine the number that, when multiplied by itself three times, gives 10000.
Answer
The cube root of $10000$ is approximately $21.54$.
Answer for screen readers
The cube root of $10000$ is approximately $21.54$.
Steps to Solve
- Set up the equation for the cube root
To find the cube root of $10000$, we want to find a number $x$ such that:
$$ x^3 = 10000 $$
- Rewrite the equation in terms of the cube root
We can express the cube root in the following manner:
$$ x = \sqrt[3]{10000} $$
- Calculate the cube root
To compute this, we can also break down $10000$ into its prime factors. We know that:
$$ 10000 = 10^4 $$
- Use the properties of exponents
Now we can apply the properties of exponents to find the cube root:
$$ \sqrt[3]{10^4} = 10^{4/3} $$
- Convert to a mixed fraction
The exponent $4/3$ can be expressed as a mixed number:
$$ 10^{4/3} = 10^{1 + 1/3} = 10^1 \cdot 10^{1/3} = 10 \cdot \sqrt[3]{10} $$
- Approximate the cube root
Next, we can find the approximate value of $\sqrt[3]{10}$. It is around $2.154$. So we multiply:
$$ 10 \cdot 2.154 \approx 21.54 $$
The cube root of $10000$ is approximately $21.54$.
More Information
The cube root function is often used in various fields of math and science, including engineering and physics. The number $10$ raised to the power of $4$, which gives us $10000$, shows how exponential growth can relate to larger numbers.
Tips
One common mistake is to confuse the cube root with the square root. Be careful to use the correct root depending on what the question specifies.
Another mistake is trying to calculate the cube root directly without breaking down the number into its prime factors, which can make it difficult to solve correctly.