Use A Calculator To Evaluate The Following Expression. Round Your Answer To The Nearest Thousandth.$\ln \sqrt{18}$Type Your Numerical Answer Below.$\square$

Introduction

In this article, we will explore the concept of evaluating the natural logarithm of a square root, specifically the expression $\ln \sqrt{18}$. We will use a calculator to find the numerical value of this expression and round it to the nearest thousandth.

Understanding the Expression

The expression $\ln \sqrt{18}$ involves two mathematical operations: the square root and the natural logarithm. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we are taking the square root of 18. The natural logarithm, denoted by $\ln$, is the inverse operation of the exponential function. It returns the power to which a base (in this case, the base is the mathematical constant $e$) must be raised to produce a given number.

Step 1: Evaluate the Square Root

To evaluate the square root of 18, we can use a calculator or perform the calculation manually. The square root of 18 is approximately 4.243.

import math

# Calculate the square root of 18
square_root = math.sqrt(18)
print(square_root)

Step 2: Evaluate the Natural Logarithm

Now that we have the value of the square root, we can evaluate the natural logarithm of this value. We can use a calculator or perform the calculation manually. The natural logarithm of 4.243 is approximately 1.435.

import math

# Calculate the natural logarithm of the square root of 18
natural_logarithm = math.log(4.243)
print(natural_logarithm)

Rounding the Answer to the Nearest Thousandth

Finally, we need to round the answer to the nearest thousandth. This means that we need to round the value of the natural logarithm to three decimal places.

import math

# Round the natural logarithm to the nearest thousandth
rounded_answer = round(natural_logarithm, 3)
print(rounded_answer)

Conclusion

In this article, we evaluated the natural logarithm of a square root using a calculator. We first calculated the square root of 18, then evaluated the natural logarithm of this value, and finally rounded the answer to the nearest thousandth. The final answer is approximately 1.435.

Final Answer

Q: What is the natural logarithm of a square root?

A: The natural logarithm of a square root is a mathematical expression that involves two operations: the square root and the natural logarithm. The square root of a number is a value that, when multiplied by itself, gives the original number. The natural logarithm, denoted by $\ln$, is the inverse operation of the exponential function. It returns the power to which a base (in this case, the base is the mathematical constant $e$) must be raised to produce a given number.

Q: How do I evaluate the natural logarithm of a square root?

A: To evaluate the natural logarithm of a square root, you need to follow these steps:

1. Calculate the square root of the given number.
2. Evaluate the natural logarithm of the square root.
3. Round the answer to the nearest thousandth.

Q: What is the difference between the natural logarithm and the common logarithm?

A: The natural logarithm and the common logarithm are two different mathematical operations. The natural logarithm, denoted by $\ln$, is the inverse operation of the exponential function and returns the power to which the base $e$ must be raised to produce a given number. The common logarithm, denoted by $\log$, is the inverse operation of the exponential function and returns the power to which the base 10 must be raised to produce a given number.

Q: Can I use a calculator to evaluate the natural logarithm of a square root?

A: Yes, you can use a calculator to evaluate the natural logarithm of a square root. Most calculators have a built-in function for calculating the natural logarithm and the square root. You can simply enter the expression $\ln \sqrt{18}$ into the calculator and press the "Enter" button to get the result.

Q: How do I round the answer to the nearest thousandth?

A: To round the answer to the nearest thousandth, you need to look at the digit in the thousandths place. If it is 5 or greater, you round up. If it is less than 5, you round down.

Q: What is the final answer to the expression $\ln \sqrt{18}$?

A: The final answer to the expression $\ln \sqrt{18}$ is approximately 1.435.

Q: Can I use a programming language to evaluate the natural logarithm of a square root?

A: Yes, you can use a programming language such as Python to evaluate the natural logarithm of a square root. You can use the math module in Python to calculate the square root and the natural logarithm.

Q: How do I calculate the square root of a number in a programming language?

A: To calculate the square root of a number in a programming language, you can use the math.sqrt() function. For example, in Python, you can use the following code to calculate the square root of 18:

import math

square_root = math.sqrt(18)
print(square_root)

Q: How do I calculate the natural logarithm of a number in a programming language?

A: To calculate the natural logarithm of a number in a programming language, you can use the math.log() function. For example, in Python, you can use the following code to calculate the natural logarithm of 4.243:

import math

natural_logarithm = math.log(4.243)
print(natural_logarithm)

Conclusion

In this article, we answered some frequently asked questions about evaluating the natural logarithm of a square root. We covered topics such as the definition of the natural logarithm of a square root, how to evaluate it, and how to round the answer to the nearest thousandth. We also discussed how to use a calculator and a programming language to evaluate the natural logarithm of a square root.