Solve For { Z $} . . . { \sqrt[3]{z} = 10 \}

Introduction

In this article, we will delve into the world of mathematics and explore a fundamental concept in algebra: solving for z in the equation $\sqrt[3]{z} = 10$. This equation involves a cube root, which is a fundamental operation in mathematics that can be used to solve a wide range of problems. We will break down the solution step by step, providing a clear and concise explanation of each step.

Understanding the Equation

The given equation is $\sqrt[3]{z} = 10$. To solve for z, we need to isolate z on one side of the equation. The cube root of a number is a value that, when multiplied by itself three times, gives the original number. In this case, we are looking for a value of z such that the cube root of z is equal to 10.

Step 1: Cube Both Sides of the Equation

To solve for z, we need to get rid of the cube root on the left-hand side of the equation. We can do this by cubing both sides of the equation. This will eliminate the cube root and give us an equation with z as the subject.

$\sqrt[3]{z} = 10$

Cubing both sides of the equation gives us:

$z = 10^3$

Step 3: Simplify the Right-Hand Side of the Equation

Now that we have cubed both sides of the equation, we can simplify the right-hand side. $10^3$ is equal to 1000.

$z = 1000$

Conclusion

In this article, we have solved for z in the equation $\sqrt[3]{z} = 10$. We started by understanding the equation and then cubed both sides to eliminate the cube root. Finally, we simplified the right-hand side of the equation to find the value of z. The final answer is $z = 1000$.

Frequently Asked Questions

• What is the cube root of a number? The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
• How do you solve for z in the equation $\sqrt[3]{z} = 10$? To solve for z, you need to cube both sides of the equation and then simplify the right-hand side.
• What is the value of z in the equation $\sqrt[3]{z} = 10$? The value of z is 1000.

Real-World Applications

Solving for z in the equation $\sqrt[3]{z} = 10$ has many real-world applications. For example, in engineering, you may need to calculate the volume of a cube or the length of a side of a cube. In finance, you may need to calculate the future value of an investment or the interest rate on a loan. In science, you may need to calculate the density of a substance or the pressure of a gas.

Tips and Tricks

• When solving for z in the equation $\sqrt[3]{z} = 10$, make sure to cube both sides of the equation.
• When simplifying the right-hand side of the equation, make sure to use the correct exponent.
• When applying the solution to real-world problems, make sure to use the correct units and formulas.

Conclusion

In conclusion, solving for z in the equation $\sqrt[3]{z} = 10$ is a fundamental concept in algebra that has many real-world applications. By following the steps outlined in this article, you can solve for z and apply the solution to a wide range of problems. Remember to cube both sides of the equation and simplify the right-hand side to find the value of z.

Introduction

In our previous article, we explored the concept of solving for z in the equation $\sqrt[3]{z} = 10$. We broke down the solution step by step, providing a clear and concise explanation of each step. In this article, we will answer some of the most frequently asked questions about solving for z in the equation $\sqrt[3]{z} = 10$.

Q&A

Q: What is the cube root of a number?

A: The cube root of a number is a value that, when multiplied by itself three times, gives the original number.

Q: How do you solve for z in the equation $\sqrt[3]{z} = 10$?

A: To solve for z, you need to cube both sides of the equation and then simplify the right-hand side.

Q: What is the value of z in the equation $\sqrt[3]{z} = 10$?

A: The value of z is 1000.

Q: Can you explain the concept of cubing a number?

A: Yes, cubing a number means multiplying the number by itself three times. For example, $2^3 = 2 \times 2 \times 2 = 8$.

Q: How do you simplify the right-hand side of the equation?

A: To simplify the right-hand side of the equation, you need to use the correct exponent. In this case, $10^3 = 1000$.

Q: What are some real-world applications of solving for z in the equation $\sqrt[3]{z} = 10$?

A: Solving for z in the equation $\sqrt[3]{z} = 10$ has many real-world applications, including calculating the volume of a cube, the length of a side of a cube, the future value of an investment, and the interest rate on a loan.

Q: Can you provide an example of how to apply the solution to a real-world problem?

A: Yes, here's an example: Suppose you want to calculate the volume of a cube with a side length of 10 cm. To do this, you would need to cube the side length, which would give you the volume of the cube. Using the equation $\sqrt[3]{z} = 10$, you can solve for z and then cube the result to get the volume of the cube.

Q: What are some common mistakes to avoid when solving for z in the equation $\sqrt[3]{z} = 10$?

A: Some common mistakes to avoid when solving for z in the equation $\sqrt[3]{z} = 10$ include:

• Not cubing both sides of the equation
• Not simplifying the right-hand side of the equation
• Using the wrong exponent
• Not checking the units of the answer

Conclusion

In conclusion, solving for z in the equation $\sqrt[3]{z} = 10$ is a fundamental concept in algebra that has many real-world applications. By following the steps outlined in this article and avoiding common mistakes, you can solve for z and apply the solution to a wide range of problems.

Additional Resources

• For more information on solving for z in the equation $\sqrt[3]{z} = 10$, check out our previous article.
• For more information on real-world applications of solving for z in the equation $\sqrt[3]{z} = 10$, check out our article on "Real-World Applications of Solving for z in the Equation $\sqrt[3]{z} = 10$".
• For more information on common mistakes to avoid when solving for z in the equation $\sqrt[3]{z} = 10$, check out our article on "Common Mistakes to Avoid When Solving for z in the Equation $\sqrt[3]{z} = 10$".