Problem 18 - Prealgebra

Question

Use a calculator to find each square root to the nearest tenth. $$-\sqrt{86}$$

Step-by-Step Solution

Answer

Approximately -9.3.

Step 1: Understand the Exercise

We need to find the square root of 86 and then apply the negative sign. This means we need to calculate \(\sqrt{86}\).

Step 2: Use a Calculator

Input 86 into your calculator to find \(\sqrt{86}\), which is approximately 9.2736.

Step 3: Round to the Nearest Tenth

Take the result 9.2736 and round it to the nearest tenth, which gives us 9.3.

Step 4: Apply the Negative Sign

Apply the negative sign to the rounded value: \(-9.3\).

Key Concepts

Calculator Usage

When tackling square root problems, a calculator can be your best friend. Calculators are designed to handle complex calculations quickly and accurately. This is especially handy when dealing with square roots of non-perfect squares, like 86. Here's how you can efficiently use your calculator for these tasks:

• Make sure your calculator is in the correct mode, usually standard mode for basic operations.
• To find the square root of a number, look for the square root button, usually represented by the symbol \(\sqrt{ }\).
• Enter the number you wish to find the square root of, in this case, 86, and press the square root button to compute it.
• Carefully record the output. For \(\sqrt{86}\), most calculators will display approximately 9.2736.

Using a calculator eliminates the risk of manual calculation errors, providing a reliable result to proceed with rounding and further operations.

Rounding Decimals

Understanding how to round decimals is crucial when dealing with any numerical solutions, particularly when precision is needed to a certain decimal place. Rounding decimals involves tweaking the number to make it shorter or simpler while keeping it reasonably close to the original value. Here's a quick guide on rounding to the nearest tenth, as required in the exercise:

• Identify the digit in the tenths place, which is the first digit to the right of the decimal point. In 9.2736, this digit is 2.
• Look at the next digit, in the hundredths place, which is 7 in this number.
• If the hundredths digit is 5 or higher, round the tenths digit up by one. Since 7 is greater than 5, increase 2 to 3, resulting in a rounded value of 9.3.
• Drop the remaining digits after the tenths place to finalize your rounded number.

Learning to round correctly ensures that you retain as much accuracy as needed for the problem at hand, while simplifying the dataset for clarity.

Negative Numbers

Negative numbers can sometimes seem intimidating, but with a little practice, they become easier to understand. After finding the square root of a number and rounding it, applying a negative sign is simple:

• Take the final result from your calculations (including any rounding or approximations).
• Attach a negative sign directly in front of that result. In our example, after rounding \(\sqrt{86}\) to 9.3, the negative number becomes \(-9.3\).
• Remember, the negative sign simply indicates that the value is less than zero, placing it on the number line below zero.

Understanding negative numbers is essential, especially when dealing with mathematical operations that represent opposites, deficits, or when reflecting positive values across zero.