Solve For $h$.$\sqrt{h+14} = 8$h =$

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Understanding the Problem

Solving for $h$ in the equation $\sqrt{h+14} = 8$ requires careful manipulation of the equation to isolate the variable $h$. This problem involves working with square roots and algebraic expressions, which are fundamental concepts in mathematics.

Step 1: Square Both Sides of the Equation

To eliminate the square root, we can square both sides of the equation. This will allow us to simplify the expression and isolate the variable $h$. Squaring both sides of the equation $\sqrt{h+14} = 8$ gives us:

$$\left(\sqrt{h+14}\right)^2 = 8^2$$

Step 2: Simplify the Equation

Squaring both sides of the equation results in:

$$h+14 = 64$$

Step 3: Isolate the Variable $h$

To isolate the variable $h$, we need to get rid of the constant term $14$ on the left-hand side of the equation. We can do this by subtracting $14$ from both sides of the equation:

$$h+14-14 = 64-14$$

Step 4: Simplify the Equation

Simplifying the equation gives us:

$$h = 50$$

Conclusion

By carefully manipulating the equation and isolating the variable $h$, we have found the solution to the problem. The value of $h$ is $50$.

Final Answer

The final answer is $\boxed{50}$.

Understanding the Solution

The solution to the problem involves working with square roots and algebraic expressions. By squaring both sides of the equation and isolating the variable $h$, we were able to find the value of $h$. This problem requires a strong understanding of algebraic concepts and the ability to manipulate equations to isolate variables.

Real-World Applications

This problem has real-world applications in various fields, such as physics and engineering. For example, in physics, the equation $\sqrt{h+14} = 8$ may represent the height of an object above the ground, where $h$ is the height of the object and $14$ is the initial height. By solving for $h$, we can determine the final height of the object.

Tips and Tricks

When working with square roots and algebraic expressions, it's essential to be careful when manipulating equations. Make sure to square both sides of the equation and isolate the variable correctly to avoid errors.

Common Mistakes

One common mistake when solving this problem is to forget to square both sides of the equation. This can result in an incorrect solution. Another mistake is to not isolate the variable $h$ correctly, which can also lead to an incorrect solution.

Additional Resources

For more practice problems and resources on solving equations with square roots, check out the following websites:

• Khan Academy: Solving Equations with Square Roots
• Mathway: Solving Equations with Square Roots

Conclusion

Solving for $h$ in the equation $\sqrt{h+14} = 8$ requires careful manipulation of the equation to isolate the variable $h$. By squaring both sides of the equation and isolating the variable $h$, we were able to find the value of $h$. This problem has real-world applications in various fields and requires a strong understanding of algebraic concepts.

Frequently Asked Questions

Q: What is the first step in solving an equation with a square root?

A: The first step in solving an equation with a square root is to square both sides of the equation. This will eliminate the square root and allow you to simplify the expression.

Q: Why do I need to square both sides of the equation?

A: Squaring both sides of the equation is necessary to eliminate the square root. If you don't square both sides, you will be left with an equation that contains a square root, which can be difficult to solve.

Q: How do I know when to square both sides of the equation?

A: You should square both sides of the equation when you see a square root on one side of the equation. This will allow you to eliminate the square root and simplify the expression.

Q: What is the next step after squaring both sides of the equation?

A: After squaring both sides of the equation, you should simplify the expression by combining like terms. This will help you isolate the variable and solve for its value.

Q: How do I isolate the variable in an equation with a square root?

A: To isolate the variable in an equation with a square root, you should use inverse operations to get rid of the constant term on the same side of the equation as the variable. This will allow you to solve for the value of the variable.

Q: What are some common mistakes to avoid when solving equations with square roots?

A: Some common mistakes to avoid when solving equations with square roots include forgetting to square both sides of the equation, not simplifying the expression, and not isolating the variable correctly.

Q: How can I practice solving equations with square roots?

A: You can practice solving equations with square roots by working through example problems and exercises. You can also use online resources, such as Khan Academy and Mathway, to get additional practice and support.

Q: What are some real-world applications of solving equations with square roots?

A: Solving equations with square roots has many real-world applications, including physics, engineering, and finance. For example, in physics, the equation $\sqrt{h+14} = 8$ may represent the height of an object above the ground, where $h$ is the height of the object and $14$ is the initial height.

Q: How can I use technology to help me solve equations with square roots?

A: You can use technology, such as calculators and computer software, to help you solve equations with square roots. These tools can help you simplify expressions and isolate variables, making it easier to solve for the value of the variable.

Q: What are some tips for solving equations with square roots?

A: Some tips for solving equations with square roots include being careful when squaring both sides of the equation, simplifying the expression, and isolating the variable correctly. You should also use inverse operations to get rid of the constant term on the same side of the equation as the variable.

Additional Resources

For more practice problems and resources on solving equations with square roots, check out the following websites:

• Khan Academy: Solving Equations with Square Roots
• Mathway: Solving Equations with Square Roots

Conclusion

Solving equations with square roots requires careful manipulation of the equation to isolate the variable. By squaring both sides of the equation and simplifying the expression, you can solve for the value of the variable. This problem has many real-world applications and requires a strong understanding of algebraic concepts.