Which Equation Is Equivalent To $\sqrt{x}+11=15$?A. $x+11=225$B. $x+121=225$C. $\sqrt{x}=15+11$D. $\sqrt{x}=15-11$

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Understanding the Given Equation

The given equation is $\sqrt{x}+11=15$. This equation involves a square root term and a constant term. To find an equivalent equation, we need to isolate the variable $x$ and simplify the equation.

Isolating the Square Root Term

To isolate the square root term, we need to subtract 11 from both sides of the equation. This will give us:

$$\sqrt{x} = 15 - 11$$

Simplifying the Equation

Now, we can simplify the equation by evaluating the expression on the right-hand side:

$$\sqrt{x} = 4$$

Squaring Both Sides

To eliminate the square root term, we can square both sides of the equation. This will give us:

$$x = 4^2$$

Evaluating the Expression

Now, we can evaluate the expression on the right-hand side:

$$x = 16$$

Checking the Answer Choices

Let's check the answer choices to see which one is equivalent to the given equation.

Answer Choice A: $x+11=225$

To check if this answer choice is equivalent, we need to subtract 11 from both sides of the equation:

$$x = 225 - 11$$

$$x = 214$$

This is not equivalent to the given equation.

Answer Choice B: $x+121=225$

To check if this answer choice is equivalent, we need to subtract 121 from both sides of the equation:

$$x = 225 - 121$$

$$x = 104$$

This is not equivalent to the given equation.

Answer Choice C: $\sqrt{x}=15+11$

To check if this answer choice is equivalent, we need to simplify the expression on the right-hand side:

$$\sqrt{x} = 26$$

This is not equivalent to the given equation.

Answer Choice D: $\sqrt{x}=15-11$

To check if this answer choice is equivalent, we need to simplify the expression on the right-hand side:

$$\sqrt{x} = 4$$

This is equivalent to the given equation.

Conclusion

The correct answer is D. $\sqrt{x}=15-11$. This answer choice is equivalent to the given equation $\sqrt{x}+11=15$.

Step-by-Step Solution

1. Isolate the square root term by subtracting 11 from both sides of the equation.
2. Simplify the equation by evaluating the expression on the right-hand side.
3. Square both sides of the equation to eliminate the square root term.
4. Evaluate the expression on the right-hand side.
5. Check the answer choices to see which one is equivalent to the given equation.

Tips and Tricks

• When working with square root terms, it's often helpful to isolate the square root term first.
• When simplifying an equation, make sure to evaluate any expressions on the right-hand side.
• When squaring both sides of an equation, make sure to simplify the resulting expression.

Common Mistakes

• Failing to isolate the square root term before simplifying the equation.
• Failing to evaluate expressions on the right-hand side when simplifying the equation.
• Failing to simplify the resulting expression when squaring both sides of the equation.

Real-World Applications

• The concept of isolating square root terms and simplifying equations is used in a variety of real-world applications, including physics, engineering, and computer science.
• The ability to work with square root terms and simplify equations is an important skill for anyone working in a field that involves mathematical modeling or problem-solving.

Further Reading

• For more information on working with square root terms and simplifying equations, see the following resources:
• Khan Academy: Square Roots
• Mathway: Square Root Equations
• Wolfram MathWorld: Square Root

Conclusion

In conclusion, the correct answer is D. $\sqrt{x}=15-11$. This answer choice is equivalent to the given equation $\sqrt{x}+11=15$. By following the step-by-step solution and tips and tricks outlined in this article, you should be able to solve similar equations and understand the concept of isolating square root terms and simplifying equations.

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Frequently Asked Questions

Q: What is the given equation?

A: The given equation is $\sqrt{x}+11=15$.

Q: What is the goal of the problem?

A: The goal of the problem is to find an equivalent equation to the given equation.

Q: How do I isolate the square root term?

A: To isolate the square root term, subtract 11 from both sides of the equation.

Q: What is the simplified equation after isolating the square root term?

A: The simplified equation is $\sqrt{x} = 15 - 11$.

Q: What is the value of the square root term?

A: The value of the square root term is 4.

Q: How do I eliminate the square root term?

A: To eliminate the square root term, square both sides of the equation.

Q: What is the resulting equation after squaring both sides?

A: The resulting equation is $x = 4^2$.

Q: What is the value of x?

A: The value of x is 16.

Q: Which answer choice is equivalent to the given equation?

A: The correct answer choice is D. $\sqrt{x}=15-11$.

Q: Why is answer choice D correct?

A: Answer choice D is correct because it is equivalent to the given equation $\sqrt{x}+11=15$.

Q: What are some common mistakes to avoid when working with square root terms?

A: Some common mistakes to avoid when working with square root terms include failing to isolate the square root term, failing to evaluate expressions on the right-hand side, and failing to simplify the resulting expression.

Q: What are some real-world applications of working with square root terms?

A: Some real-world applications of working with square root terms include physics, engineering, and computer science.

Q: Where can I find more information on working with square root terms?

A: You can find more information on working with square root terms at the following resources:

• Khan Academy: Square Roots
• Mathway: Square Root Equations
• Wolfram MathWorld: Square Root

Additional Questions and Answers

Q: Can I use a calculator to solve this problem?

A: Yes, you can use a calculator to solve this problem. However, it's often helpful to work through the problem step-by-step to understand the concept.

Q: How do I know which answer choice is correct?

A: To determine which answer choice is correct, work through the problem step-by-step and compare your answer to the answer choices.

Q: Can I use a different method to solve this problem?

A: Yes, you can use a different method to solve this problem. However, the method outlined in this article is a common and effective way to solve this type of problem.

Q: What if I get stuck on a problem like this?

A: If you get stuck on a problem like this, try breaking it down into smaller steps, or ask for help from a teacher or tutor.

Conclusion

In conclusion, the correct answer is D. $\sqrt{x}=15-11$. This answer choice is equivalent to the given equation $\sqrt{x}+11=15$. By following the step-by-step solution and tips and tricks outlined in this article, you should be able to solve similar equations and understand the concept of isolating square root terms and simplifying equations.