Evaluating the Cube Root of 8

Oct 13, 2025 by leolavanderia.com.br 68 views

Introduction

In this problem, we are given an equation $s^3 = 8$ and we need to find the value of $s$ . This is a simple equation, but it can be solved using various methods. We will use the method of taking the cube root of both sides of the equation to find the value of $s$ .

Method 1: Taking the Cube Root of Both Sides

To solve the equation $s^3 = 8$ , we can take the cube root of both sides of the equation. This will give us the value of $s$ .

$s^3 = 8$

$\sqrt[3]{s^3} = \sqrt[3]{8}$

$s = \sqrt[3]{8}$

Evaluating the Cube Root of 8

The cube root of 8 can be evaluated as follows:

$\sqrt[3]{8} = \sqrt[3]{2^3}$

$= 2$

Therefore, the value of $s$ is 2.

Checking the Answer

To check our answer, we can substitute the value of $s$ back into the original equation.

$s^3 = 8$

$(2)^3 = 8$

$8 = 8$

This shows that our answer is correct.

Conclusion

In this problem, we used the method of taking the cube root of both sides of the equation to find the value of $s$ . We evaluated the cube root of 8 and found that it is equal to 2. We then checked our answer by substituting the value of $s$ back into the original equation.

Alternative Solutions

There are alternative solutions to this problem. We can also use the method of factoring to solve the equation.

$s^3 - 8 = 0$

$(s - 2)(s^2 + 2s + 4) = 0$

This gives us two possible solutions: $s = 2$ or $s^2 + 2s + 4 = 0$ .

However, the quadratic equation $s^2 + 2s + 4 = 0$ has no real solutions, so we can ignore it.

Discussion

This problem is a simple example of how to solve an equation using the method of taking the cube root of both sides. It is an important concept in algebra and is used to solve equations of the form $x^n = a$ , where $n$ is a positive integer and $a$ is a real number.

Real-World Applications

This problem has real-world applications in various fields such as physics, engineering, and computer science. For example, in physics, the equation $s^3 = 8$ can be used to describe the motion of an object that is moving in a cubic path.

Conclusion

In conclusion, we have solved the equation $s^3 = 8$ using the method of taking the cube root of both sides. We evaluated the cube root of 8 and found that it is equal to 2. We then checked our answer by substituting the value of $s$ back into the original equation. This problem is an important example of how to solve equations using algebraic methods.

Final Answer

The final answer is: $\boxed{2}$

Introduction

In our previous article, we solved the equation $s^3 = 8$ using the method of taking the cube root of both sides. We found that the value of $s$ is 2. In this article, we will provide a Q&A section to help readers understand the problem and its solution.

Q&A

Q: What is the equation $s^3 = 8$ ?

A: The equation $s^3 = 8$ is a cubic equation where $s$ is the variable and 8 is the constant.

Q: How do we solve the equation $s^3 = 8$ ?

A: We can solve the equation $s^3 = 8$ by taking the cube root of both sides of the equation.

Q: What is the cube root of 8?

A: The cube root of 8 is 2.

Q: How do we check our answer?

A: We can check our answer by substituting the value of $s$ back into the original equation.

Q: What is the final answer?

A: The final answer is 2.

Q: Can we use other methods to solve the equation $s^3 = 8$ ?

A: Yes, we can use other methods such as factoring to solve the equation $s^3 = 8$ . However, the method of taking the cube root of both sides is the simplest and most straightforward method.

Q: What are the real-world applications of solving the equation $s^3 = 8$ ?

A: Solving the equation $s^3 = 8$ has real-world applications in various fields such as physics, engineering, and computer science.

Q: Can we solve the equation $s^3 = 8$ using a calculator?

A: Yes, we can solve the equation $s^3 = 8$ using a calculator. However, it is always a good idea to understand the underlying math and to check our answer using the method of substitution.

Conclusion

In this Q&A article, we have provided answers to common questions related to the equation $s^3 = 8$ . We have explained how to solve the equation using the method of taking the cube root of both sides and how to check our answer. We have also discussed the real-world applications of solving the equation and how to use a calculator to solve it.

Final Answer

The final answer is: $\boxed{2}$