Evaluate 3 0.008 {}^3 \sqrt{0.008} 3 0.008 ​ .a. 0.04 B. 0.4 C. 0.02 D. 0.2 Please Select The Best Answer From The Choices Provided.

Understanding the Problem

In this problem, we are asked to evaluate the cube root of 0.008. The cube root of a number is a value that, when multiplied by itself three times, gives the original number. In mathematical notation, this is represented as ${}^3 \sqrt{x}$, where $x$ is the number inside the cube root.

The Formula for Cube Root

The formula for the cube root of a number is:

${}^3 \sqrt{x} = \sqrt[3]{x}$

This formula tells us that to find the cube root of a number, we need to raise that number to the power of $\frac{1}{3}$.

Evaluating the Cube Root of 0.008

Now that we understand the formula for the cube root, let's apply it to the number 0.008.

${}^3 \sqrt{0.008} = \sqrt[3]{0.008}$

To evaluate this expression, we need to raise 0.008 to the power of $\frac{1}{3}$.

Raising a Decimal Number to a Power

When we raise a decimal number to a power, we need to follow the rules of exponentiation. In this case, we need to raise 0.008 to the power of $\frac{1}{3}$.

To do this, we can use the fact that $0.008 = 8 \times 10^{-3}$. Then, we can raise this expression to the power of $\frac{1}{3}$.

${}^3 \sqrt{0.008} = \sqrt[3]{8 \times 10^{-3}}$

Using the properties of exponents, we can rewrite this expression as:

${}^3 \sqrt{0.008} = (8 \times 10^{-3})^{\frac{1}{3}}$

Simplifying the Expression

Now that we have raised 0.008 to the power of $\frac{1}{3}$, we can simplify the expression.

$(8 \times 10^{-3})^{\frac{1}{3}} = 2 \times 10^{-1}$

Evaluating the Expression

Finally, we can evaluate the expression by multiplying 2 by $10^{-1}$.

$2 \times 10^{-1} = 0.2$

Conclusion

In conclusion, the cube root of 0.008 is 0.2.

Answer

The correct answer is:

• d. 0.2

Discussion

This problem requires us to apply the formula for the cube root of a number and to raise a decimal number to a power. It also requires us to follow the rules of exponentiation and to simplify the expression.

Related Topics

• Cube Root Formula: The formula for the cube root of a number is ${}^3 \sqrt{x} = \sqrt[3]{x}$.
• Exponentiation: Exponentiation is the process of raising a number to a power.
• Decimal Numbers: Decimal numbers are numbers that have a decimal point.

Practice Problems

• Evaluate ${}^3 \sqrt{0.064}$.
• Evaluate ${}^3 \sqrt{0.001}$.
• Evaluate ${}^3 \sqrt{0.216}$.

Solutions

• Evaluate ${}^3 \sqrt{0.064}$: The cube root of 0.064 is 0.4.
• Evaluate ${}^3 \sqrt{0.001}$: The cube root of 0.001 is 0.1.
• Evaluate ${}^3 \sqrt{0.216}$: The cube root of 0.216 is 0.6.
  Evaluating the Cube Root of a Decimal Number: Q&A =====================================================

Q: What is the cube root of a decimal number?

A: The cube root of a decimal number is a value that, when multiplied by itself three times, gives the original number. In mathematical notation, this is represented as ${}^3 \sqrt{x}$, where $x$ is the number inside the cube root.

Q: How do I evaluate the cube root of a decimal number?

A: To evaluate the cube root of a decimal number, you need to raise that number to the power of $\frac{1}{3}$. This can be done using the formula:

${}^3 \sqrt{x} = \sqrt[3]{x}$

Q: What is the formula for the cube root of a number?

A: The formula for the cube root of a number is:

${}^3 \sqrt{x} = \sqrt[3]{x}$

Q: How do I raise a decimal number to a power?

A: When you raise a decimal number to a power, you need to follow the rules of exponentiation. In this case, you need to raise the decimal number to the power of $\frac{1}{3}$.

Q: Can I use a calculator to evaluate the cube root of a decimal number?

A: Yes, you can use a calculator to evaluate the cube root of a decimal number. Most calculators have a cube root button that you can use to find the cube root of a number.

Q: What is the cube root of 0.008?

A: The cube root of 0.008 is 0.2.

Q: What is the cube root of 0.064?

A: The cube root of 0.064 is 0.4.

Q: What is the cube root of 0.001?

A: The cube root of 0.001 is 0.1.

Q: What is the cube root of 0.216?

A: The cube root of 0.216 is 0.6.

Q: Can I use the cube root formula to find the cube root of a negative number?

A: No, you cannot use the cube root formula to find the cube root of a negative number. The cube root of a negative number is not a real number.

Q: Can I use the cube root formula to find the cube root of a fraction?

A: Yes, you can use the cube root formula to find the cube root of a fraction. To do this, you need to simplify the fraction first.

Q: What is the cube root of $\frac{1}{8}$?

A: The cube root of $\frac{1}{8}$ is $\frac{1}{2}$.

Q: What is the cube root of $\frac{27}{64}$?

A: The cube root of $\frac{27}{64}$ is $\frac{3}{4}$.

Q: Can I use the cube root formula to find the cube root of a decimal number with a negative exponent?

A: No, you cannot use the cube root formula to find the cube root of a decimal number with a negative exponent. The cube root of a decimal number with a negative exponent is not a real number.

Q: Can I use the cube root formula to find the cube root of a decimal number with a fractional exponent?

A: Yes, you can use the cube root formula to find the cube root of a decimal number with a fractional exponent. To do this, you need to simplify the expression first.

Q: What is the cube root of $0.008^{\frac{1}{2}}$?

A: The cube root of $0.008^{\frac{1}{2}}$ is $0.2^{\frac{1}{2}}$.

Q: What is the cube root of $0.064^{\frac{1}{3}}$?

A: The cube root of $0.064^{\frac{1}{3}}$ is $0.4^{\frac{1}{3}}$.

Q: What is the cube root of $0.001^{\frac{1}{4}}$?

A: The cube root of $0.001^{\frac{1}{4}}$ is $0.1^{\frac{1}{4}}$.

Q: Can I use the cube root formula to find the cube root of a decimal number with a variable exponent?

A: No, you cannot use the cube root formula to find the cube root of a decimal number with a variable exponent. The cube root of a decimal number with a variable exponent is not a real number.

Q: Can I use the cube root formula to find the cube root of a decimal number with a complex exponent?

A: No, you cannot use the cube root formula to find the cube root of a decimal number with a complex exponent. The cube root of a decimal number with a complex exponent is not a real number.

Q: What is the cube root of $0.008^{\frac{1}{3} + \frac{1}{2}}$?

A: The cube root of $0.008^{\frac{1}{3} + \frac{1}{2}}$ is $0.2^{\frac{1}{3} + \frac{1}{2}}$.

Q: What is the cube root of $0.064^{\frac{1}{3} - \frac{1}{2}}$?

A: The cube root of $0.064^{\frac{1}{3} - \frac{1}{2}}$ is $0.4^{\frac{1}{3} - \frac{1}{2}}$.

Q: What is the cube root of $0.001^{\frac{1}{4} + \frac{1}{3}}$?

A: The cube root of $0.001^{\frac{1}{4} + \frac{1}{3}}$ is $0.1^{\frac{1}{4} + \frac{1}{3}}$.

Q: Can I use the cube root formula to find the cube root of a decimal number with a mixed exponent?

A: Yes, you can use the cube root formula to find the cube root of a decimal number with a mixed exponent. To do this, you need to simplify the expression first.

Q: What is the cube root of $0.008^{\frac{1}{3} + \frac{1}{2} + \frac{1}{4}}$?

A: The cube root of $0.008^{\frac{1}{3} + \frac{1}{2} + \frac{1}{4}}$ is $0.2^{\frac{1}{3} + \frac{1}{2} + \frac{1}{4}}$.

Q: What is the cube root of $0.064^{\frac{1}{3} - \frac{1}{2} + \frac{1}{4}}$?

A: The cube root of $0.064^{\frac{1}{3} - \frac{1}{2} + \frac{1}{4}}$ is $0.4^{\frac{1}{3} - \frac{1}{2} + \frac{1}{4}}$.

Q: What is the cube root of $0.001^{\frac{1}{4} + \frac{1}{3} - \frac{1}{2}}$?

A: The cube root of $0.001^{\frac{1}{4} + \frac{1}{3} - \frac{1}{2}}$ is $0.1^{\frac{1}{4} + \frac{1}{3} - \frac{1}{2}}$.

Conclusion

In conclusion, the cube root of a decimal number is a value that, when multiplied by itself three times, gives the original number. To evaluate the cube root of a decimal number, you need to raise that number to the power of $\frac{1}{3}$. This can be done using the formula:

${}^3 \sqrt{x} = \sqrt[3]{x}$

Answer

The correct answers are:

• The cube root of 0.008 is 0.2.
• The cube root of 0.064 is 0.4.
• The cube root of 0.001 is 0.1.
• The cube root of 0.216 is 0.6.
• The cube root of $\frac{1}{8}$ is $\frac{1}{2}$.
• The cube root of $\frac{27}{64}$ is $\frac{3}{4}$.
• The cube root of $0.008^{\frac{1}{2}}$ is $0.2^{\frac{1}{2}}$.
• The cube root of $0.064^{\frac{1}{3}}$ is $0.4^{\frac{1}{3}}$.
• **The cube root of $0.001^{\frac{