Jamal Simplified The Expression 75 X 5 Y 8 \sqrt{75 X^5 Y^8} 75 X 5 Y 8 ​ Where X ≥ 0 X \geq 0 X ≥ 0 And Y ≥ 0 Y \geq 0 Y ≥ 0 . 75 X 5 Y 8 = 25 ⋅ 3 ⋅ X 4 ⋅ X ⋅ Y 8 = 5 X 2 Y 2 3 X \sqrt{75 X^5 Y^8} = \sqrt{25 \cdot 3 \cdot X^4 \cdot X \cdot Y^8} = 5 X^2 Y^2 \sqrt{3 X} 75 X 5 Y 8 ​ = 25 ⋅ 3 ⋅ X 4 ⋅ X ⋅ Y 8 ​ = 5 X 2 Y 2 3 X ​ Which Describes The Error Jamal Made?A. He

Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a deep understanding of the underlying concepts. In this article, we will analyze Jamal's attempt to simplify the expression $\sqrt{75 x^5 y^8}$ and identify the error he made. We will also provide a step-by-step guide on how to simplify the expression correctly.

The Original Expression

The original expression is $\sqrt{75 x^5 y^8}$. This expression involves the square root of a product of numbers and variables. To simplify this expression, we need to use the properties of radicals.

Jamal's Attempt

Jamal attempted to simplify the expression as follows:

$\sqrt{75 x^5 y^8} = \sqrt{25 \cdot 3 \cdot x^4 \cdot x \cdot y^8} = 5 x^2 y^2 \sqrt{3 x}$

However, Jamal's attempt is incorrect. Let's analyze the error he made.

Error Analysis

The error Jamal made is in the simplification of the expression. He incorrectly applied the property of radicals, which states that $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$. In this case, Jamal should have applied this property to the expression $\sqrt{25 \cdot 3 \cdot x^4 \cdot x \cdot y^8}$.

Correct Simplification

To simplify the expression correctly, we need to apply the property of radicals as follows:

$\sqrt{75 x^5 y^8} = \sqrt{25 \cdot 3 \cdot x^4 \cdot x \cdot y^8} = \sqrt{25} \cdot \sqrt{x^4} \cdot \sqrt{x} \cdot \sqrt{3} \cdot \sqrt{y^8}$

Using the property of radicals, we can simplify each radical as follows:

$\sqrt{25} = 5$ $\sqrt{x^4} = x^2$ $\sqrt{x} = x$ $\sqrt{3} = \sqrt{3}$ $\sqrt{y^8} = y^4$

Therefore, the correct simplification of the expression is:

$\sqrt{75 x^5 y^8} = 5 x^2 y^4 \sqrt{3 x}$

Conclusion

In conclusion, Jamal's attempt to simplify the expression $\sqrt{75 x^5 y^8}$ was incorrect. He incorrectly applied the property of radicals, which led to an incorrect simplification of the expression. The correct simplification of the expression is $5 x^2 y^4 \sqrt{3 x}$.

Step-by-Step Guide

To simplify the expression $\sqrt{75 x^5 y^8}$, follow these steps:

1. Factor the expression under the radical sign into its prime factors.
2. Apply the property of radicals to each factor.
3. Simplify each radical using the properties of radicals.
4. Combine the simplified radicals to obtain the final answer.

By following these steps, you can simplify the expression $\sqrt{75 x^5 y^8}$ correctly.

Common Mistakes

When simplifying algebraic expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

• Incorrectly applying the property of radicals.
• Failing to simplify each radical.
• Not combining the simplified radicals correctly.

By being aware of these common mistakes, you can avoid them and simplify algebraic expressions correctly.

Practice Problems

To practice simplifying algebraic expressions, try the following problems:

• Simplify the expression $\sqrt{16 x^6 y^9}$.
• Simplify the expression $\sqrt{9 x^4 y^7}$.
• Simplify the expression $\sqrt{25 x^3 y^5}$.

By practicing these problems, you can improve your skills in simplifying algebraic expressions.

Conclusion

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Introduction

In our previous article, we analyzed Jamal's attempt to simplify the expression $\sqrt{75 x^5 y^8}$ and identified the error he made. In this article, we will provide a Q&A section to help you understand the concepts and techniques involved in simplifying algebraic expressions.

Q&A Section

Q: What is the property of radicals?

A: The property of radicals states that $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$. This means that we can simplify a product of numbers and variables under a radical sign by taking the square root of each factor separately.

Q: How do I apply the property of radicals?

A: To apply the property of radicals, you need to factor the expression under the radical sign into its prime factors. Then, take the square root of each factor separately and combine them.

Q: What is the difference between $\sqrt{x^4}$ and $x^2$?

A: $\sqrt{x^4}$ and $x^2$ are not the same thing. $\sqrt{x^4}$ is the square root of $x^4$, which is equal to $x^2$. However, $x^2$ is simply $x$ squared, not the square root of $x$.

Q: How do I simplify a radical expression?

A: To simplify a radical expression, you need to apply the property of radicals and simplify each radical separately. You can use the following steps:

1. Factor the expression under the radical sign into its prime factors.
2. Take the square root of each factor separately.
3. Combine the simplified radicals.

Q: What is the correct simplification of $\sqrt{75 x^5 y^8}$?

A: The correct simplification of $\sqrt{75 x^5 y^8}$ is $5 x^2 y^4 \sqrt{3 x}$.

Q: What are some common mistakes to avoid when simplifying algebraic expressions?

A: Some common mistakes to avoid when simplifying algebraic expressions include:

• Incorrectly applying the property of radicals.
• Failing to simplify each radical.
• Not combining the simplified radicals correctly.

Q: How can I practice simplifying algebraic expressions?

A: You can practice simplifying algebraic expressions by trying the following problems:

• Simplify the expression $\sqrt{16 x^6 y^9}$.
• Simplify the expression $\sqrt{9 x^4 y^7}$.
• Simplify the expression $\sqrt{25 x^3 y^5}$.

Q: What are some real-world applications of simplifying algebraic expressions?

A: Simplifying algebraic expressions has many real-world applications, including:

• Calculating distances and velocities in physics.
• Modeling population growth and decay in biology.
• Solving optimization problems in economics.

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill in mathematics. By understanding the properties of radicals and applying them correctly, you can simplify expressions like $\sqrt{75 x^5 y^8}$. Remember to avoid common mistakes and practice simplifying expressions to improve your skills.

Additional Resources

For more information on simplifying algebraic expressions, check out the following resources:

• Khan Academy: Simplifying Radical Expressions
• Mathway: Simplifying Radical Expressions
• Wolfram Alpha: Simplifying Radical Expressions

By using these resources, you can improve your skills in simplifying algebraic expressions and apply them to real-world problems.