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Chapter 8: Problem 70

Use a calculator to approximate the square root to three decimal places. $$\sqrt{50,416,000}$$

Short Answer

Expert verified
7093.088

Step by step solution

01

- Identify the Operation

The problem asks for the square root of 50,416,000.
02

- Use a Calculator

Using a scientific calculator, input the number 50,416,000 and press the square root function (usually represented by \(\sqrt{}\)).
03

- Approximate to Three Decimal Places

The calculator will provide an initial result. Round this result to three decimal places for precision.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Calculator Usage
A calculator can simplify complex mathematical operations like finding square roots. For this exercise, we focus on using a calculator to approximate square roots. Start by turning on your calculator. All calculators have basic functions, whether they are a simple or a scientific calculator. Input the number 50,416,000 and press the square root function, often represented as \(\backslash \textbackslashsqrt{}\). This function quickly performs the square root operation, providing an initial result. Remember to always ensure you're entering the correct number to avoid errors.
Scientific Calculator
A scientific calculator is a powerful tool that helps in performing advanced mathematical operations. It includes functions not usually found in basic calculators. When calculating the square root of a number like 50,416,000, the scientific calculator simplifies the process. First, look for the square root button labeled \(\backslash \textbackslashsqrt{}\) or a similar symbol. Enter the number accurately, ensuring you use any necessary commas or decimal points. Then press the square root button, and the calculator will display the initial result. Using a scientific calculator minimizes human error and speeds up calculations.
Decimal Places
Rounding to specific decimal places is vital for precision in mathematical calculations. In this exercise, we approximate the square root of 50,416,000 to three decimal places. Let's say the calculator shows an initial result of 7093.380217. To round this to three decimal places, we focus on the first four digits after the decimal point. Since the fourth digit (2) is less than 5, we don't need to round up the third digit. Thus, our final approximated result is 7093.380. Rounding ensures our answer is clear and consistent.

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