Squaring both sides of the equation

Oct 13, 2025 by windailys.com 4 views

Introduction

In this article, we will delve into solving for $u$ in the equation $\sqrt{u} = 10$ . This equation involves a square root, which can be solved by isolating the variable $u$ . We will explore the steps involved in solving this equation and provide the solution(s) for $u$ .

Understanding the Equation

The given equation is $\sqrt{u} = 10$ . This equation states that the square root of $u$ is equal to 10. To solve for $u$ , we need to isolate the variable $u$ and find its value.

Solving the Equation

To solve the equation $\sqrt{u} = 10$ , we can start by squaring both sides of the equation. This will eliminate the square root and allow us to solve for $u$ .

$\sqrt{u} = 10$

Squaring both sides of the equation:

$u = 10^2$

$u = 100$

Therefore, the solution to the equation $\sqrt{u} = 10$ is $u = 100$ .

Checking the Solution

To verify that the solution $u = 100$ is correct, we can substitute it back into the original equation.

$\sqrt{u} = 10$

Substituting $u = 100$ :

$\sqrt{100} = 10$

$10 = 10$

Since the equation holds true, we can confirm that the solution $u = 100$ is correct.

Conclusion

In this article, we have solved for $u$ in the equation $\sqrt{u} = 10$ . By squaring both sides of the equation, we were able to isolate the variable $u$ and find its value. The solution to the equation is $u = 100$ . This demonstrates the importance of following the order of operations and using algebraic techniques to solve equations involving square roots.

Additional Tips and Tricks

When solving equations involving square roots, it's essential to remember the following tips and tricks:

Squaring both sides of the equation: This is a common technique used to eliminate the square root and solve for the variable.
Checking the solution: Always verify that the solution satisfies the original equation to ensure its correctness.
Using algebraic techniques: Algebraic techniques, such as factoring and simplifying expressions, can be used to solve equations involving square roots.

By following these tips and tricks, you can become proficient in solving equations involving square roots and tackle more complex problems with confidence.

Frequently Asked Questions

What is the solution to the equation $\sqrt{u} = 10$ ?
- The solution to the equation $\sqrt{u} = 10$ is $u = 100$ .
How do I solve equations involving square roots?
- To solve equations involving square roots, you can use algebraic techniques, such as squaring both sides of the equation, to eliminate the square root and solve for the variable.
Why is it essential to check the solution?
- It's essential to check the solution to ensure that it satisfies the original equation and is correct.

Final Thoughts

Solving equations involving square roots requires a combination of algebraic techniques and attention to detail. By following the steps outlined in this article and using the tips and tricks provided, you can become proficient in solving these types of equations and tackle more complex problems with confidence.

Introduction

In our previous article, we explored solving for $u$ in the equation $\sqrt{u} = 10$ . We delved into the steps involved in solving this equation and provided the solution(s) for $u$ . In this article, we will continue to provide more information and answer frequently asked questions related to solving equations involving square roots.

Q&A

Q: What is the solution to the equation $\sqrt{u} = 10$ ?

A: The solution to the equation $\sqrt{u} = 10$ is $u = 100$ .

Q: How do I solve equations involving square roots?

A: To solve equations involving square roots, you can use algebraic techniques, such as squaring both sides of the equation, to eliminate the square root and solve for the variable.

Q: Why is it essential to check the solution?

A: It's essential to check the solution to ensure that it satisfies the original equation and is correct.

Q: What if the equation has more than one solution?

A: If the equation has more than one solution, you can separate the solutions with commas. For example, if the equation is $\sqrt{u} = 10$ and $u = 100$ and $u = -100$ , the solutions would be $u = 100, -100$ .

Q: What if the equation has no solution?

A: If the equation has no solution, you can indicate this by saying "No solution" or "There is no solution".

Q: Can I use other algebraic techniques to solve equations involving square roots?

A: Yes, you can use other algebraic techniques, such as factoring and simplifying expressions, to solve equations involving square roots.

Q: How do I know which algebraic technique to use?

A: The choice of algebraic technique depends on the specific equation and the variable you are solving for. You can try different techniques and see which one works best.

Q: Can I use a calculator to solve equations involving square roots?

A: Yes, you can use a calculator to solve equations involving square roots. However, it's essential to understand the underlying algebraic techniques and be able to apply them manually.

Q: What if I get stuck while solving an equation involving a square root?

A: If you get stuck while solving an equation involving a square root, try breaking down the problem into smaller steps, and use algebraic techniques to simplify the equation.

Additional Tips and Tricks

Practice, practice, practice: The more you practice solving equations involving square roots, the more comfortable you will become with the algebraic techniques and the more confident you will be in your ability to solve these types of equations.
Use online resources: There are many online resources available that can help you learn how to solve equations involving square roots, including video tutorials, practice problems, and interactive quizzes.
Seek help when needed: Don't be afraid to ask for help if you are struggling with a particular equation or concept. Your teacher, tutor, or classmate may be able to provide additional guidance and support.

Conclusion

Frequently Asked Questions

What is the solution to the equation $\sqrt{u} = 10$ ?
- The solution to the equation $\sqrt{u} = 10$ is $u = 100$ .
How do I solve equations involving square roots?
- To solve equations involving square roots, you can use algebraic techniques, such as squaring both sides of the equation, to eliminate the square root and solve for the variable.
Why is it essential to check the solution?
- It's essential to check the solution to ensure that it satisfies the original equation and is correct.

Final Thoughts

Solving equations involving square roots requires patience, persistence, and practice. By following the steps outlined in this article and using the tips and tricks provided, you can become proficient in solving these types of equations and tackle more complex problems with confidence.