Simplify $\sqrt{0.08^{12}}$.A. $(0.08)^6$ B. $(0.8)^6$ C. $(0.16)^6$ D. $(0.12)^8$ Please Select The Best Answer From The Choices Provided: A B C D

Introduction

Radical expressions, also known as roots, are an essential part of mathematics, particularly in algebra and geometry. They are used to represent the square root, cube root, and other roots of numbers. In this article, we will focus on simplifying radical expressions, specifically the expression $\sqrt{0.08^{12}}$. We will explore the properties of radical expressions and provide a step-by-step guide on how to simplify this expression.

Understanding Radical Expressions

A radical expression is a mathematical expression that contains a root, such as a square root or cube root. The root is denoted by a symbol, such as $\sqrt{}$ for the square root or $\sqrt[3]{}$ for the cube root. Radical expressions can be simplified using various properties and rules.

Properties of Radical Expressions

There are several properties of radical expressions that can be used to simplify them. These properties include:

• Product Property: $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$
• Quotient Property: $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$
• Power Property: $\sqrt{a^b} = a^{\frac{b}{2}}$

Simplifying $\sqrt{0.08^{12}}$

To simplify the expression $\sqrt{0.08^{12}}$, we can use the power property of radical expressions. This property states that $\sqrt{a^b} = a^{\frac{b}{2}}$. We can rewrite the expression as:

$$\sqrt{0.08^{12}} = (0.08)^{\frac{12}{2}}$$

Using the power property, we can simplify the expression further:

$$(0.08)^{\frac{12}{2}} = (0.08)^6$$

Therefore, the simplified expression is $(0.08)^6$.

Comparing with the Options

Now that we have simplified the expression, we can compare it with the options provided:

• A. $(0.08)^6$
• B. $(0.8)^6$
• C. $(0.16)^6$
• D. $(0.12)^8$

Based on our simplification, we can see that the correct answer is:

A. $(0.08)^6$

Conclusion

Simplifying radical expressions is an essential skill in mathematics, particularly in algebra and geometry. By understanding the properties of radical expressions and using the power property, we can simplify complex expressions like $\sqrt{0.08^{12}}$. In this article, we have provided a step-by-step guide on how to simplify this expression and compared it with the options provided. We hope that this article has been helpful in understanding the concept of simplifying radical expressions.

Additional Tips and Resources

• For more information on radical expressions, please refer to the following resources:

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

• To practice simplifying radical expressions, please try the following exercises:

• Simplify $\sqrt{0.16^{12}}$
• Simplify $\sqrt{0.24^{18}}$
• Simplify $\sqrt{0.36^{24}}$

Final Answer

Introduction

In our previous article, we explored the concept of simplifying radical expressions, specifically the expression $\sqrt{0.08^{12}}$. We provided a step-by-step guide on how to simplify this expression and compared it with the options provided. In this article, we will continue to provide more information and answer frequently asked questions about simplifying radical expressions.

Q&A: Simplifying Radical Expressions

Q: What is the difference between a radical expression and a rational expression?

A: A radical expression is a mathematical expression that contains a root, such as a square root or cube root. A rational expression, on the other hand, is a mathematical expression that contains a fraction, such as $\frac{a}{b}$.

Q: How do I simplify a radical expression with a negative exponent?

A: To simplify a radical expression with a negative exponent, you can use the property $\sqrt{a^{-b}} = \frac{1}{\sqrt{a^b}}$. For example, $\sqrt{0.08^{-6}} = \frac{1}{\sqrt{0.08^6}}$.

Q: Can I simplify a radical expression with a decimal number?

A: Yes, you can simplify a radical expression with a decimal number. For example, $\sqrt{0.08^{12}} = (0.08)^6$. However, be careful when simplifying decimal numbers, as they can sometimes lead to incorrect answers.

Q: How do I simplify a radical expression with a variable?

A: To simplify a radical expression with a variable, you can use the property $\sqrt{a^b} = a^{\frac{b}{2}}$. For example, $\sqrt{x^{12}} = x^6$.

Q: Can I simplify a radical expression with a negative number?

A: Yes, you can simplify a radical expression with a negative number. For example, $\sqrt{(-0.08)^{12}} = (0.08)^6$. However, be careful when simplifying negative numbers, as they can sometimes lead to incorrect answers.

Q: How do I simplify a radical expression with a fraction?

A: To simplify a radical expression with a fraction, you can use the property $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$. For example, $\sqrt{\frac{0.08}{0.16}} = \frac{\sqrt{0.08}}{\sqrt{0.16}}$.

Q: Can I simplify a radical expression with a complex number?

A: Yes, you can simplify a radical expression with a complex number. However, this is a more advanced topic and requires a good understanding of complex numbers.

Conclusion

Simplifying radical expressions is an essential skill in mathematics, particularly in algebra and geometry. By understanding the properties of radical expressions and using the power property, we can simplify complex expressions like $\sqrt{0.08^{12}}$. In this article, we have provided a Q&A guide on how to simplify radical expressions and answered frequently asked questions.

Additional Tips and Resources

• For more information on radical expressions, please refer to the following resources:

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

• To practice simplifying radical expressions, please try the following exercises:

• Simplify $\sqrt{0.16^{12}}$
• Simplify $\sqrt{0.24^{18}}$
• Simplify $\sqrt{0.36^{24}}$

Final Answer

The final answer is: A