Identify The Errors Lewis Made. Check All That Apply.1. He Simplified \[$\sqrt{400}\$\] Incorrectly; It Should Be 20 Instead Of 200.2. He Found The Difference Between The Hypotenuse And The Short Leg Instead Of The Long Leg.3. He Evaluated
Identifying Errors in Lewis's Math Problem
Math problems can be challenging, and even the smallest mistake can lead to incorrect solutions. In this article, we will analyze a math problem and identify the errors made by Lewis. We will examine each step of the problem and provide a detailed explanation of the mistakes.
The Math Problem
The math problem in question is as follows:
- Find the length of the long leg of a right triangle with a hypotenuse of 20 and a short leg of 12.
Step 1: Simplifying the Square Root
The first step in solving the problem is to simplify the square root of 400. Lewis incorrectly simplified it to 200 instead of 20.
Why is 20 the correct answer?
The square root of 400 can be simplified by finding the largest perfect square that divides 400. In this case, 400 = 20^2. Therefore, the square root of 400 is 20, not 200.
Step 2: Finding the Difference between the Hypotenuse and the Short Leg
The next step in solving the problem is to find the length of the long leg. However, Lewis found the difference between the hypotenuse and the short leg instead of the long leg.
Why is this a mistake?
The difference between the hypotenuse and the short leg is not the same as the length of the long leg. To find the length of the long leg, we need to use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Step 3: Evaluating the Pythagorean Theorem
The Pythagorean theorem can be used to find the length of the long leg. However, Lewis did not evaluate the theorem correctly.
Why is this a mistake?
The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is 20, and the short leg is 12. Therefore, the length of the long leg can be found using the following equation:
c^2 = a^2 + b^2
where c is the hypotenuse, a is the short leg, and b is the long leg.
Solving for b
To solve for b, we can plug in the values of a and c into the equation:
b^2 = c^2 - a^2 b^2 = 20^2 - 12^2 b^2 = 400 - 144 b^2 = 256 b = sqrt(256) b = 16
In conclusion, Lewis made several mistakes in solving the math problem. He simplified the square root of 400 incorrectly, found the difference between the hypotenuse and the short leg instead of the long leg, and did not evaluate the Pythagorean theorem correctly. By identifying these errors, we can provide a correct solution to the problem.
The correct solution to the problem is as follows:
- Simplify the square root of 400 to 20.
- Use the Pythagorean theorem to find the length of the long leg.
- Plug in the values of a and c into the equation to solve for b.
By following these steps, we can find the correct solution to the problem.
Final Answer
The final answer is 16.
Q&A: Identifying Errors in Lewis's Math Problem
In our previous article, we analyzed a math problem and identified the errors made by Lewis. We examined each step of the problem and provided a detailed explanation of the mistakes. In this article, we will answer some frequently asked questions about the problem and provide additional clarification on the errors.
Q: What is the correct way to simplify the square root of 400?
A: The correct way to simplify the square root of 400 is to find the largest perfect square that divides 400. In this case, 400 = 20^2. Therefore, the square root of 400 is 20, not 200.
Q: Why did Lewis find the difference between the hypotenuse and the short leg instead of the long leg?
A: Lewis found the difference between the hypotenuse and the short leg instead of the long leg because he did not understand the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. To find the length of the long leg, we need to use this theorem.
Q: How do we use the Pythagorean theorem to find the length of the long leg?
A: To use the Pythagorean theorem to find the length of the long leg, we need to plug in the values of a and c into the equation:
b^2 = c^2 - a^2
where c is the hypotenuse, a is the short leg, and b is the long leg.
Q: What is the correct solution to the problem?
A: The correct solution to the problem is as follows:
- Simplify the square root of 400 to 20.
- Use the Pythagorean theorem to find the length of the long leg.
- Plug in the values of a and c into the equation to solve for b.
Q: What are some common mistakes to avoid when solving math problems?
A: Some common mistakes to avoid when solving math problems include:
- Simplifying expressions incorrectly
- Not understanding the Pythagorean theorem
- Not plugging in values correctly into equations
- Not checking units and dimensions
Q: How can we improve our math skills and avoid making mistakes?
A: To improve our math skills and avoid making mistakes, we can:
- Practice regularly and consistently
- Review and understand the basics of math
- Ask for help when needed
- Check our work and double-check our answers
In conclusion, identifying errors in math problems is an important skill to develop. By understanding the mistakes made by Lewis, we can improve our own math skills and avoid making similar mistakes. We hope this Q&A article has provided additional clarification on the errors and has helped to improve your understanding of the problem.
If you are struggling with math problems or need additional help, there are many resources available. Some of these resources include:
- Online math tutorials and videos
- Math textbooks and workbooks
- Math apps and software
- Tutoring services and online communities
We hope this article has been helpful in identifying errors in Lewis's math problem and has provided additional clarification on the errors. If you have any further questions or need additional help, please don't hesitate to ask.