# 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.

The cube root of $10000$ is approximately $21.54$.

The cube root of $10000$ is approximately $21.54$.

#### Steps to Solve

1. Set up the equation for the cube root

To find the cube root of $10000$, we want to find a number $x$ such that:

$$x^3 = 10000$$

1. Rewrite the equation in terms of the cube root

We can express the cube root in the following manner:

$$x = \sqrt[3]{10000}$$

1. Calculate the cube root

To compute this, we can also break down $10000$ into its prime factors. We know that:

$$10000 = 10^4$$

1. Use the properties of exponents

Now we can apply the properties of exponents to find the cube root:

$$\sqrt[3]{10^4} = 10^{4/3}$$

1. Convert to a mixed fraction

The exponent $4/3$ can be expressed as a mixed number:

$$10^{4/3} = 10^{1 + 1/3} = 10^1 \cdot 10^{1/3} = 10 \cdot \sqrt[3]{10}$$

1. 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 $21.54$.

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.

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