Select The Correct Answer.Simplify The Following Algebraic Expression: 5 A C 2 \sqrt{5 A C^2} 5 A C 2 ​ A. 6 T 2 9 6 T^2 \sqrt{9} 6 T 2 9 ​ B. 3 Π T 4 3 \sqrt{\pi T^4} 3 Π T 4 ​ C. 9 T 2 6 9 T^2 \sqrt{6} 9 T 2 6 ​ D. 3 T 2 6 3 T^2 \sqrt{6} 3 T 2 6 ​

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill to master. In this article, we will focus on simplifying the algebraic expression $\sqrt{5 A C^2}$ and provide a step-by-step guide on how to select the correct answer.

Understanding the Expression

The given expression is $\sqrt{5 A C^2}$. To simplify this expression, we need to understand the properties of square roots. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we have $\sqrt{5 A C^2}$, which means we need to find a value that, when multiplied by itself, gives $5 A C^2$.

Breaking Down the Expression

To simplify the expression, we can break it down into smaller parts. We can start by identifying the variables and constants in the expression. In this case, we have:

• $5$: a constant
• $A$: a variable
• $C$: a variable
• $^2$: a power of 2

We can rewrite the expression as $\sqrt{5} \cdot \sqrt{A^2} \cdot \sqrt{C^2}$.

Simplifying the Expression

Now that we have broken down the expression, we can simplify it further. We know that $\sqrt{A^2} = A$ and $\sqrt{C^2} = C$. Therefore, we can rewrite the expression as $\sqrt{5} \cdot A \cdot C$.

Evaluating the Options

Now that we have simplified the expression, we can evaluate the options. We have:

A. $6 t^2 \sqrt{9}$ B. $3 \sqrt{\pi t^4}$ C. $9 t^2 \sqrt{6}$ D. $3 t^2 \sqrt{6}$

To select the correct answer, we need to compare the simplified expression with each option.

Comparing the Options

Let's compare the simplified expression $\sqrt{5} \cdot A \cdot C$ with each option:

• Option A: $6 t^2 \sqrt{9}$. This option does not match the simplified expression.
• Option B: $3 \sqrt{\pi t^4}$. This option does not match the simplified expression.
• Option C: $9 t^2 \sqrt{6}$. This option does not match the simplified expression.
• Option D: $3 t^2 \sqrt{6}$. This option does not match the simplified expression.

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill to master. In our previous article, we provided a step-by-step guide on how to simplify the algebraic expression $\sqrt{5 A C^2}$. In this article, we will provide a Q&A guide to help you understand the concept better.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way to represent a mathematical relationship between variables and constants.

Q: What is the square root of a number?

A: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to follow these steps:

1. Identify the variables and constants in the expression.
2. Break down the expression into smaller parts.
3. Simplify each part using the properties of square roots.
4. Combine the simplified parts to get the final expression.

Q: What are the properties of square roots?

A: The properties of square roots are:

• $\sqrt{a^2} = a$
• $\sqrt{b^2} = b$
• $\sqrt{c^2} = c$
• $\sqrt{d^2} = d$

Q: How do I apply the properties of square roots to simplify an expression?

A: To apply the properties of square roots, you need to identify the variables and constants in the expression and break it down into smaller parts. Then, you can simplify each part using the properties of square roots.

Q: What is the final expression after simplifying $\sqrt{5 A C^2}$?

A: The final expression after simplifying $\sqrt{5 A C^2}$ is $\sqrt{5} \cdot A \cdot C$.

Q: How do I evaluate the options to select the correct answer?

A: To evaluate the options, you need to compare the simplified expression with each option. If the simplified expression matches one of the options, then that option is the correct answer.

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

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

• Not identifying the variables and constants in the expression.
• Not breaking down the expression into smaller parts.
• Not applying the properties of square roots correctly.
• Not combining the simplified parts correctly.

Conclusion

Simplifying algebraic expressions is an essential skill to master in mathematics. By following the steps outlined in this article and avoiding common mistakes, you can simplify algebraic expressions with confidence. Remember to identify the variables and constants, break down the expression into smaller parts, simplify each part using the properties of square roots, and combine the simplified parts to get the final expression.

Frequently Asked Questions

• Q: What is the square root of a number? A: The square root of a number is a value that, when multiplied by itself, gives the original number.
• Q: How do I simplify an algebraic expression? A: To simplify an algebraic expression, you need to follow these steps: identify the variables and constants, break down the expression into smaller parts, simplify each part using the properties of square roots, and combine the simplified parts.
• Q: What are the properties of square roots? A: The properties of square roots are: $\sqrt{a^2} = a$, $\sqrt{b^2} = b$, $\sqrt{c^2} = c$, and $\sqrt{d^2} = d$.
• Q: How do I apply the properties of square roots to simplify an expression? A: To apply the properties of square roots, you need to identify the variables and constants in the expression and break it down into smaller parts. Then, you can simplify each part using the properties of square roots.
• Q: What is the final expression after simplifying $\sqrt{5 A C^2}$? A: The final expression after simplifying $\sqrt{5 A C^2}$ is $\sqrt{5} \cdot A \cdot C$.
• Q: How do I evaluate the options to select the correct answer? A: To evaluate the options, you need to compare the simplified expression with each option. If the simplified expression matches one of the options, then that option is the correct answer.