Problem 37 - Elementary and Intermediate Algebra

Question

Use a calculator to find each square root. Give each answer to four decimal places. See Objective 1. $$ \sqrt{679.25} $$

Step-by-Step Solution

Answer

The square root of 679.25 is approximately 26.0556.

Step 1: Understand the Problem

The task is to find the square root of 679.25 and provide the answer to four decimal places.

Step 2: Use a Calculator

Input the value 679.25 into a scientific calculator and apply the square root function (usually represented by a √ symbol).

Step 3: Record the Answer

Once the calculator performs the calculation, it will display the square root of 679.25. Note this value carefully.

Step 4: Round the Answer

Ensure that the answer from the calculator is rounded correctly to four decimal places by checking the fifth decimal place to see if rounding is necessary.

Key Concepts

Calculator Usage

Using a calculator is an essential skill in mathematics education, especially when dealing with complex calculations like finding the square root. A calculator simplifies the process and eliminates the possibility of manual errors. Here's how you can effectively use one for this task:

• First, make sure you have a scientific calculator, as it includes the square root function. This function is typically represented by the symbol \( \sqrt{} \).
• Turn on your calculator and input the given number, here it's 679.25.
• Locate the square root button and press it. The calculator will automatically perform the calculation.
• Once the result is displayed, your task is to write it down accurately, especially if you need to express it in specific decimal places.

Practicing with a calculator can enhance your speed and confidence when tackling different math problems. It's beneficial to familiarize yourself with all available functions, as they are incredibly helpful during exams and assignments.

Decimal Places

After obtaining the result from the calculator, it's crucial to understand how to round the number to the desired decimal places. In this case, you need to round the square root of 679.25 to four decimal places. Here's a simple guide:

• The square root of 679.25 is approximately 26.057874. Now, focus on the first four decimal places: 26.0578.
• To check if this should be rounded, look at the fifth decimal place. Here it's a 7, which is more than 5, so you should increase the last of the four decimal places by one.
• This results in the final rounded number: 26.0579.

Understanding decimal places is vital as it ensures precision and accuracy in your calculations. By grasping this concept, you can avoid mistakes in mathematical problems and represent numbers correctly.

Mathematics Education

Mathematics education involves not only learning formulas and functions but also understanding how to apply these skills effectively. When working with problems like finding square roots, several educational aspects come into play:

• **Conceptual Understanding**: It’s important to understand what a square root represents, which is a number that, when multiplied by itself, gives the original number. Grasping this helps you predict whether your calculated answer seems reasonable.
• **Practical Application**: Using calculators to solve real-world problems is a practical skill. Mathematics education teaches you when and how to apply these tools effectively.
• **Critical Thinking**: Interpreting the results and understanding rounding rules demand critical thinking. Educational frameworks aim to develop these skills, turning numerical findings into meaningful insights.

A solid foundation in these areas not only aids academic success but also prepares you for real-life scenarios where mathematical problems are presented.