Problem 38 - Intermediate Algebra

Question

Use a calculator to find each square root. Give each answer to four decimal places. See Objective 1. $$ \sqrt{0.0063} $$

Step-by-Step Solution

Answer

The square root of 0.0063 is approximately 0.0794.

Step 1: Identify the Expression

We begin by identifying the mathematical expression we need to solve. In this case, it is finding the square root of 0.0063, represented as \( \sqrt{0.0063} \).

Step 2: Use a Calculator

Enter the number 0.0063 into a calculator and apply the square root function to determine its value. Make sure your calculator is set to display at least four decimal places to fulfill the requirement of this exercise.

Step 3: Record and Round the Result

The calculator will display the result, which is approximately 0.079366. Round this number to four decimal places to get an accurate answer: 0.0794.

Step 4: Conclusion

To summarize, the square root of 0.0063 is approximately 0.0794 when rounded to four decimal places.

Key Concepts

Calculator Usage

Using a calculator can make finding square roots quick and easy. Let's first understand how to enter the square root function into your calculator. Most basic calculators will have a square root button often symbolized as \( \sqrt{} \) or "√". If you’re using a scientific calculator, this button is typically located on the number pad.

Here's a simple step-by-step to use it:

• Turn on your calculator and clear any previous entries to avoid confusion.
• Enter the number for which you want to find the square root. In this exercise, the number is 0.0063.
• Press the square root button. On some calculators, you might need to enter the number first, followed by the "\( \sqrt{} \)" function.
• The calculator will then display the square root of the entered number.

By learning these key steps, you can efficiently verify results for homework and avoid unnecessary mistakes when dealing with square roots.

Decimal Places

Decimal places are essential when it comes to precision in mathematics. They refer to the number of digits to the right of the decimal point. In scientific and academic settings, specifying a fixed number of decimal places helps ensure consistency and accuracy of data.

In the original exercise, you need to provide your final answer to four decimal places. This means when the calculator gives you a result like 0.079366, your answer should show only four digits after the decimal point, like this: 0.0794.

Some scenarios where specifying decimal places is important include:

• When measuring precise quantities in experiments.
• In financial calculations, where currencies might need exactness.
• Handling smaller numbers, especially when small errors can significantly affect the result.

Understanding decimal places ensures your calculations are both accurate and in line with the required precision.

Rounding Numbers

Rounding numbers is a process used to reduce the digits in a number while keeping its value relatively close to the original. It is often used in various practical applications when exact precision is not needed, or when it improves readability.

Here’s how you round a number to a specific number of decimal places, like our example from the original exercise:

• First, look at the digit immediately following the last required decimal place.
• If that digit is 5 or higher, increase the last required decimal place by one. For example, rounding 0.079366 to four decimal places results in 0.0794 because the sixth digit is 6, which is above 5.
• If that digit is lower than 5, keep the existing digit as it is, without any changes.

This rounding rule helps maintain consistency, and it can be applied to numerous types of calculations across various disciplines. It’s an essential skill to develop for academic success.