Which Expression Is Equivalent To $4 X^{\overline{2}}$?A. $2 \sqrt{x}$ B. \$4 \sqrt{x}$[/tex\] C. $\sqrt{4 X}$ D. $\frac{1}{\sqrt{4 X}}$

The given expression is $4 x^{\overline{2}}$. To understand this expression, we need to know what the notation $x^{\overline{2}}$ means. In this notation, the bar over the exponent 2 indicates that the exponent is to be taken as the number of times we multiply the base $x$ by itself, and then we take the square root of the result.

In other words, $x^{\overline{2}}$ is equivalent to $\sqrt{x^2}$. This is because the square root of a number is the same as raising that number to the power of $\frac{1}{2}$.

So, the given expression $4 x^{\overline{2}}$ can be rewritten as $4 \sqrt{x^2}$.

Rewriting the Expression

Now, let's rewrite the expression $4 \sqrt{x^2}$ in a more familiar form. We know that $\sqrt{x^2} = |x|$, where $|x|$ is the absolute value of $x$. Therefore, we can rewrite the expression as $4 |x|$.

However, we are given four options, and none of them match the expression $4 |x|$. Let's examine each option carefully.

Option A: $2 \sqrt{x}$

Option A is $2 \sqrt{x}$. This expression is not equivalent to $4 x^{\overline{2}}$. To see why, let's compare the two expressions. The expression $4 x^{\overline{2}}$ is equivalent to $4 \sqrt{x^2}$, which is equal to $4 |x|$. On the other hand, the expression $2 \sqrt{x}$ is equal to $2 |x|$. As we can see, the two expressions are not equivalent.

Option B: $4 \sqrt{x}$

Option B is $4 \sqrt{x}$. This expression is not equivalent to $4 x^{\overline{2}}$. To see why, let's compare the two expressions. The expression $4 x^{\overline{2}}$ is equivalent to $4 \sqrt{x^2}$, which is equal to $4 |x|$. On the other hand, the expression $4 \sqrt{x}$ is equal to $4 \sqrt{|x|}$. As we can see, the two expressions are not equivalent.

Option C: $\sqrt{4 x}$

Q: What is the notation $x^{\overline{2}}$?

A: The notation $x^{\overline{2}}$ means that the exponent 2 is to be taken as the number of times we multiply the base $x$ by itself, and then we take the square root of the result.

Q: How is the expression $4 x^{\overline{2}}$ rewritten?

A: The expression $4 x^{\overline{2}}$ can be rewritten as $4 \sqrt{x^2}$.

Q: What is the meaning of $\sqrt{x^2}$?

A: $\sqrt{x^2}$ is equal to $|x|$, where $|x|$ is the absolute value of $x$.

Q: How is the expression $4 \sqrt{x^2}$ rewritten?

A: The expression $4 \sqrt{x^2}$ can be rewritten as $4 |x|$.

Q: Which of the given options is equivalent to $4 x^{\overline{2}}$?

A: None of the given options (A, B, C, D) are equivalent to $4 x^{\overline{2}}$. However, we can rewrite the expression $\sqrt{4 x}$ as $\sqrt{4} \sqrt{x}$, which is equal to $2 \sqrt{x}$.

Q: Why is option C, $\sqrt{4 x}$, not equivalent to $4 x^{\overline{2}}$?

A: Option C, $\sqrt{4 x}$, is not equivalent to $4 x^{\overline{2}}$ because it can be rewritten as $2 \sqrt{x}$, which is not equivalent to $4 x^{\overline{2}}$.

Q: What is the correct answer?

A: Unfortunately, none of the given options (A, B, C, D) are equivalent to $4 x^{\overline{2}}$. However, we can rewrite the expression $\sqrt{4 x}$ as $\sqrt{4} \sqrt{x}$, which is equal to $2 \sqrt{x}$.

Q: What is the final answer?

A: The final answer is not among the given options (A, B, C, D). However, we can rewrite the expression $\sqrt{4 x}$ as $\sqrt{4} \sqrt{x}$, which is equal to $2 \sqrt{x}$.

Conclusion

In this article, we have discussed the expression $4 x^{\overline{2}}$ and its equivalent forms. We have also examined the given options and found that none of them are equivalent to $4 x^{\overline{2}}$. However, we can rewrite the expression $\sqrt{4 x}$ as $\sqrt{4} \sqrt{x}$, which is equal to $2 \sqrt{x}$.