Problem 37 - Algebra 2

Question

Use a calculator to approximate each value to three decimal places. $$ \sqrt{129} $$

Step-by-Step Solution

Answer

\( \sqrt{129} \approx 11.357 \).

Step 1: Understand the Problem

The problem is asking you to find the square root of 129 and provide an approximate value to three decimal places.

Step 2: Use a Calculator

Input 129 into a calculator and use the square root function to compute the value of \( \sqrt{129} \).

Step 3: Find the Square Root

Upon using the calculator, you should find that the square root of 129 is approximately 11.357.

Step 4: Round to Three Decimal Places

Ensure the value from the calculator is rounded to three decimal places. In this case, 11.357 is already rounded to three decimal places.

Key Concepts

Calculator Use

Using a calculator is a helpful tool when you need to find the square root of a number. Calculators are especially useful for large numbers like 129, where manual calculation can be complicated. To find the square root using a calculator, here is a simple process:

• Enter the number you need the square root for. In this case, input 129.
• Find the square root function button. This is typically represented by a radical symbol (√) on most calculators.
• Press the square root button after inputting your number. The calculator will display the approximate square root.

In our example, the calculator shows approximately 11.357 as the square root of 129. Ensure your calculator is set to show decimals if available to provide more precision.

Approximation

Approximation is the process of finding a value that is close enough to the actual answer for practical purposes. With square roots, exact values aren't always possible due to their sometimes infinite decimal nature. Calculators provide an approximation because they give a rounded value. The approximation involves selecting a value after performing calculations that well represent the true result. For the square root of 129, we may not know the exact value down to infinite decimals, so 11.357 works well as a practical estimate. This number is close enough to use in most mathematical operations while balancing accuracy with simplicity.

Decimal Places

Decimal places refer to the number of digits shown after a decimal point in a number. They are important when rounding numbers, as they define the level of precision. For the task of approximating square roots, setting your result to three decimal places provides a balance between precision and readability. Here's how you can manage decimal places:

• Observe the number immediately following the required decimal places. This determines rounding.
• If this number is 5 or above, increase the last required decimal by 1.
• If it is below 5, leave the decimals as they are.

For our example, the square root of 129 is calculated as 11.357. The third decimal place (7) stays because the number following it was not higher than 4. Always double-check that your calculator is set to the correct decimal format to avoid errors in representation.