Simplify:$ \frac{4}{\sqrt{5}} }$Possible Simplified Forms A. { \frac{-4 \sqrt{5 }{5}$}$ B. { \frac{4 \sqrt{5}}{5}$}$ C. ${ 4 \sqrt{5}\$}

Simplify: $\frac{4}{\sqrt{5}}$

When dealing with square roots in fractions, it's essential to understand how to simplify them. In this article, we will explore the possible simplified forms of the expression $\frac{4}{\sqrt{5}}$. We will examine each option and determine whether it is a valid simplified form.

The given expression is $\frac{4}{\sqrt{5}}$. To simplify this expression, we need to rationalize the denominator, which means removing the square root from the denominator. We can do this by multiplying both the numerator and the denominator by the square root of the denominator.

To rationalize the denominator, we multiply both the numerator and the denominator by $\sqrt{5}$.

$$\frac{4}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{4\sqrt{5}}{5}$$

Now that we have simplified the expression, let's evaluate the options.

Option A: $\frac{-4 \sqrt{5}}{5}$

This option is incorrect because we did not multiply the numerator and the denominator by a negative number. The correct simplified form is $\frac{4\sqrt{5}}{5}$, not $\frac{-4\sqrt{5}}{5}$.

Option B: $\frac{4 \sqrt{5}}{5}$

This option is correct. We multiplied the numerator and the denominator by $\sqrt{5}$, which resulted in the simplified form $\frac{4\sqrt{5}}{5}$.

Option C: $4 \sqrt{5}$

This option is incorrect because we did not remove the denominator. The correct simplified form is $\frac{4\sqrt{5}}{5}$, not $4\sqrt{5}$.

In conclusion, the correct simplified form of the expression $\frac{4}{\sqrt{5}}$ is $\frac{4\sqrt{5}}{5}$. This is achieved by rationalizing the denominator, which involves multiplying both the numerator and the denominator by the square root of the denominator. The other options are incorrect, and we should not multiply the numerator and the denominator by a negative number or remove the denominator.

The final answer is $\boxed{\frac{4\sqrt{5}}{5}}$.

When dealing with square roots in fractions, it's essential to remember the following tips and tricks:

• To rationalize the denominator, multiply both the numerator and the denominator by the square root of the denominator.
• Be careful when multiplying the numerator and the denominator by a negative number.
• Do not remove the denominator when simplifying an expression.

By following these tips and tricks, you can simplify expressions with square roots in fractions with ease.

When simplifying expressions with square roots in fractions, there are several common mistakes to avoid:

• Multiplying the numerator and the denominator by a negative number.
• Removing the denominator when simplifying an expression.
• Not rationalizing the denominator.

By avoiding these common mistakes, you can ensure that your simplified expressions are accurate and correct.

Simplifying expressions with square roots in fractions has several real-world applications:

• In physics, simplifying expressions with square roots in fractions is essential when dealing with problems involving velocity, acceleration, and force.
• In engineering, simplifying expressions with square roots in fractions is crucial when designing and building structures, such as bridges and buildings.
• In finance, simplifying expressions with square roots in fractions is necessary when calculating interest rates and investment returns.

By understanding how to simplify expressions with square roots in fractions, you can apply this knowledge to real-world problems and make informed decisions.

In conclusion, simplifying expressions with square roots in fractions is a crucial skill that has several real-world applications. By understanding how to rationalize the denominator, avoiding common mistakes, and applying this knowledge to real-world problems, you can become proficient in simplifying expressions with square roots in fractions.
Simplify: $\frac{4}{\sqrt{5}}$ - Q&A

In our previous article, we explored the possible simplified forms of the expression $\frac{4}{\sqrt{5}}$. We determined that the correct simplified form is $\frac{4\sqrt{5}}{5}$. In this article, we will answer some frequently asked questions about simplifying expressions with square roots in fractions.

Q: What is the purpose of rationalizing the denominator?

A: The purpose of rationalizing the denominator is to remove the square root from the denominator. This is achieved by multiplying both the numerator and the denominator by the square root of the denominator.

Q: Why do we multiply the numerator and the denominator by a negative number?

A: We do not multiply the numerator and the denominator by a negative number. This is a common mistake that can result in an incorrect simplified form.

Q: Can we remove the denominator when simplifying an expression?

A: No, we cannot remove the denominator when simplifying an expression. This is another common mistake that can result in an incorrect simplified form.

Q: What are some real-world applications of simplifying expressions with square roots in fractions?

A: Simplifying expressions with square roots in fractions has several real-world applications, including physics, engineering, and finance. In physics, simplifying expressions with square roots in fractions is essential when dealing with problems involving velocity, acceleration, and force. In engineering, simplifying expressions with square roots in fractions is crucial when designing and building structures, such as bridges and buildings. In finance, simplifying expressions with square roots in fractions is necessary when calculating interest rates and investment returns.

Q: How can I avoid common mistakes when simplifying expressions with square roots in fractions?

A: To avoid common mistakes when simplifying expressions with square roots in fractions, make sure to:

• Rationalize the denominator by multiplying both the numerator and the denominator by the square root of the denominator.
• Do not multiply the numerator and the denominator by a negative number.
• Do not remove the denominator when simplifying an expression.

Q: What are some tips and tricks for simplifying expressions with square roots in fractions?

A: Here are some tips and tricks for simplifying expressions with square roots in fractions:

• To rationalize the denominator, multiply both the numerator and the denominator by the square root of the denominator.
• Be careful when multiplying the numerator and the denominator by a negative number.
• Do not remove the denominator when simplifying an expression.

Q: Can I use a calculator to simplify expressions with square roots in fractions?

A: Yes, you can use a calculator to simplify expressions with square roots in fractions. However, it's essential to understand the underlying math and be able to simplify expressions without a calculator.

In conclusion, simplifying expressions with square roots in fractions is a crucial skill that has several real-world applications. By understanding how to rationalize the denominator, avoiding common mistakes, and applying this knowledge to real-world problems, you can become proficient in simplifying expressions with square roots in fractions.

For more information on simplifying expressions with square roots in fractions, check out the following resources:

• Khan Academy: Simplifying Expressions with Square Roots
• Mathway: Simplifying Expressions with Square Roots
• Wolfram Alpha: Simplifying Expressions with Square Roots

By following these resources and practicing your skills, you can become proficient in simplifying expressions with square roots in fractions.