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Chapter 8: Problem 68

Use a calculator to approximate the square root to three decimal places. $$\sqrt{3184.75}$$

Short Answer

Expert verified
Approximately 56.436

Step by step solution

01

Understand the Problem

The goal is to find the square root of the number 3184.75 and approximate it to three decimal places.
02

Input the Number into a Calculator

Turn on the calculator and enter the number 3184.75.
03

Use the Square Root Function

Press the square root (鈭�) function key on the calculator. The display should now show the square root of 3184.75.
04

Read the Result

The calculator will show the result as approximately 56.436 when rounded to three decimal places. Note down this value.

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Key Concepts

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

square root calculation
Calculating the square root of a number is all about finding a value which, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 * 3 = 9. In mathematical terms, if you want to find the square root of a number 'n', you are looking for a number 'x' such that \( x^2 = n \).
For larger and more complex numbers, doing this manually can be very challenging. That's why calculators become handy tools. Calculators are designed to perform such mathematical operations swiftly and accurately.
using a calculator
Using a calculator for square root calculations is straightforward but it's crucial to follow the steps correctly. Here鈥檚 a simple guide to get to the desired result:
  • Turn on your calculator.
  • Input the number for which you need the square root, which in this case is 3184.75.
  • Press the square root (鈭�) function key. This is usually represented by a symbol like 鈭� or a combination of key presses depending on the calculator model.
  • Your calculator should immediately display the square root of the number.
This saves time and ensures that you get the answer with high precision compared to manual calculation.
rounding decimals
Many times, the result of a square root calculation will be a long decimal number. In our example, the display might show something like 56.436004123. For simplicity and clarity, especially in homework or exams, we often round the number to a certain number of decimal places.

Here's how to round to three decimal places:
  • Identify the digit at the fourth decimal place after the point.
  • If this digit is 5 or higher, increase the third decimal place by one. If it's lower than 5, leave it as is.
In our initial example of \( \sqrt{3184.75} \), when rounding 56.436004123 to three decimal places, the '0' at the fourth decimal place means we leave the third decimal place as is, so the result is 56.436.
Understanding these steps is crucial for ensuring your calculations and results are accurate and neatly presented.

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