Which Expression Is Equivalent To 9 K \sqrt{9k} 9 K ?A. 2 3 J 2 K 6 \frac{2}{3} J^2 K^6 3 2 J 2 K 6 B. 2 J 2 3 K 6 \frac{2 J^2}{3 K^6} 3 K 6 2 J 2 C. 2 3 J 2 K 4 \frac{2}{3} J^2 K^4 3 2 J 2 K 4 D. 2 J 2 3 K 4 \frac{2 J^2}{3 K^4} 3 K 4 2 J 2

Mar 12, 2025 by ADMIN 251 views

**Simplifying Radical Expressions: A Step-by-Step Guide**

Introduction

Radical expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will explore the process of simplifying radical expressions, with a focus on the given problem: Which expression is equivalent to $\sqrt{9k}$ ? We will break down the solution step by step, using clear and concise language to ensure that readers understand the concepts and techniques involved.

Understanding Radical Expressions

A radical expression is an expression that contains a square root or a higher-order root. 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.

Simplifying Radical Expressions

To simplify a radical expression, we need to identify any perfect squares that can be factored out of the expression. A perfect square is a number that can be expressed as the product of an integer and itself. For example, 16 is a perfect square because it can be expressed as 4 multiplied by 4.

Step 1: Factor Out Perfect Squares

The given expression is $\sqrt{9k}$ . To simplify this expression, we need to factor out any perfect squares that can be found within the expression. In this case, we can factor out a perfect square of 3, because 9 is equal to 3 multiplied by 3.

Step 2: Simplify the Expression

Now that we have factored out the perfect square, we can simplify the expression by taking the square root of the remaining factor. In this case, we have $\sqrt{3^2 k}$ , which simplifies to $3\sqrt{k}$ .

Step 3: Compare with Answer Choices

Now that we have simplified the expression, we can compare it with the answer choices to determine which one is equivalent. The simplified expression is $3\sqrt{k}$ , which can be rewritten as $\frac{3\sqrt{k}}{1}$ .

Answer Choice Analysis

Let's analyze each answer choice to determine which one is equivalent to the simplified expression.

A. $\frac{2}{3} j^2 k^6$ : This answer choice is not equivalent to the simplified expression, because it contains a different coefficient and a different power of $k$ .
B. $\frac{2 j^2}{3 k^6}$ : This answer choice is not equivalent to the simplified expression, because it contains a different coefficient and a different power of $k$ .
C. $\frac{2}{3} j^2 k^4$ : This answer choice is not equivalent to the simplified expression, because it contains a different coefficient and a different power of $k$ .
D. $\frac{2 j^2}{3 k^4}$ : This answer choice is not equivalent to the simplified expression, because it contains a different coefficient and a different power of $k$ .

Conclusion

Q: What is a radical expression?

A: A radical expression is an expression that contains a square root or a higher-order root. The square root of a number is a value that, when multiplied by itself, gives the original number.

Q: How do I simplify a radical expression?

A: To simplify a radical expression, you need to identify any perfect squares that can be factored out of the expression. A perfect square is a number that can be expressed as the product of an integer and itself.

Q: What is a perfect square?

A: A perfect square is a number that can be expressed as the product of an integer and itself. For example, 16 is a perfect square because it can be expressed as 4 multiplied by 4.

Q: How do I factor out perfect squares?

A: To factor out perfect squares, you need to identify any numbers within the expression that can be expressed as the product of an integer and itself. For example, in the expression $\sqrt{9k}$ , we can factor out a perfect square of 3, because 9 is equal to 3 multiplied by 3.

Q: What is the simplified form of $\sqrt{9k}$ ?

A: The simplified form of $\sqrt{9k}$ is $3\sqrt{k}$ .

Q: How do I compare the simplified expression with answer choices?

A: To compare the simplified expression with answer choices, you need to analyze each answer choice to determine which one is equivalent to the simplified expression.

Q: What is the correct answer choice?

A: The correct answer choice is not among the options listed. However, we can rewrite the simplified expression as $\frac{3\sqrt{k}}{1}$ , which is equivalent to $\frac{3j^0\sqrt{k}}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt{k} = \frac{3}{1} \cdot \sqrt{k} = \frac{3}{1} \cdot \sqrt{k} \cdot \frac{j^0}{j0} = \frac{3j^0}{j0}\sqrt{k} = \frac{3}{1}\sqrt