Problem 37 - 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

\( \sqrt{679.25} \approx 26.0499 \) with four decimal places.

Step 1: Understand the Problem

We are tasked with finding the square root of \( 679.25 \) and rounding the result to four decimal places.

Step 2: Use a Calculator

Turn on your calculator and ensure it is in the standard mode for operation. Locate the square root function, typically denoted as \( \sqrt{} \).

Step 3: Enter the Number

Input the number 679.25 into the calculator. Make sure that you input this number in its entirety and accurately.

Step 4: Calculate the Square Root

Press the square root function button. The calculator will compute the square root of 679.25.

Step 5: Record the Result

Read the result displayed by the calculator. Ensure that you understand how to interpret the decimal output.

Step 6: Round to Four Decimal Places

Observe the decimal point and the numbers following it. In this case, the square root of 679.25 to four decimal places is 26.0499.

Key Concepts

Calculators in Mathematics

Calculators are handy tools that simplify the arithmetic operations we encounter in mathematics. They make complex calculations such as finding square roots straightforward, with just a few button presses.

• When using a calculator, always check that it is in standard or scientific mode, depending on your need. This ensures the accuracy of the operations you're performing.
• Most calculators have a dedicated button for square roots, denoted as \( \sqrt{} \). Familiarize yourself with its placement to save time during calculations.
• Entering numbers accurately is crucial. Double-check that each digit is correct before performing operations to avoid errors in results.

Using calculators not only speeds up the process but also helps in verifying the work you perform manually. However, understanding how their functions operate enhances your overall math proficiency and reliability on tools.

Rounding Decimals

Rounding decimals is a fundamental skill in mathematics that is often used to simplify numbers to a desired degree of precision. When dealing with square roots, precise rounding is vital for accuracy in results.

• Identify the position to which you want to round off. To round to four decimal places, you focus on the fifth decimal digit.
• If the fifth decimal place is 5 or greater, the fourth decimal place is increased by one. Otherwise, it remains the same.
• After rounding, ensure all following digits are removed, leaving only those up to the specified decimal place.

For example, in the solution of \( \sqrt{679.25} = 26.0498866 \), the fifth digit is '8', which is more than '5'. Thus, we increase the last displayed digit '9' by one, rounding the value to 26.0499.

Intermediate Algebra

Intermediate algebra bridges basic arithmetic concepts and more advanced mathematical disciplines. It often involves understanding and solving problems using square roots among other operations. Square roots are a recurrent topic because they frequently appear in various algebraic applications.

• Understanding square roots involves recognizing that it is a number which, when multiplied by itself, gives the original number. For example, \( \sqrt{64} \) results in 8 because \( 8 \times 8 = 64 \).
• In intermediate algebra, square roots can be applied in solving quadratic equations, analyzing functions, and even in geometry to calculate distances.
• Using technology, like calculators, to find square roots facilitates proficiency in handling real-world problems where approximations are necessary.

Grasping these concepts prepares students for higher-level mathematics and enhances their problem-solving capabilities.