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Chapter 9: Problem 27

Use a calculator to approximate to three decimal places. $$ \sqrt{183} $$

Short Answer

Expert verified
13.528

Step by step solution

01

- Understand the Problem

The task requires finding the square root of 183, which is a non-perfect square. The result should be approximated to three decimal places.
02

- Use the Calculator

Input the number 183 into the calculator and press the square root ( 鈭� ) function. Most modern calculators have a dedicated square root button.
03

- Record the Result

After pressing the square root function, the calculator will display the square root of 183. Make sure to note the full decimal value shown.
04

- Round to Three Decimal Places

Take the decimal value from the calculator and round it to three decimal places. For example, if the calculator displays 13.527749, rounding to three decimal places gives 13.528.

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Key Concepts

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

Approximating Square Roots
Approximating square roots is important when dealing with non-perfect squares. Non-perfect squares do not have exact integer square roots.
Instead, their square roots are irrational numbers that go on infinitely.
The goal here is to find a close approximation. You can achieve this by using simple methods such as guessing and checking, but the most reliable way is using a calculator.
Using a Calculator
Using a calculator to find the square root is very straightforward. Here are the steps:
  • First, turn on your calculator.
  • Next, enter the number you need the square root of, in this case, 183.
  • After that, press the square root ( 鈭� ) button. This button might be located above another button and might require using a shift or function key.
  • The calculator will then display the square root of the number entered.
For example, after inputting 183 and pressing the square root function, you might see something like 13.527749 on your calculator screen.
Rounding to Decimal Places
Rounding to decimal places is a valuable skill when dealing with approximations. This involves simplifying a number to a set number of decimal points for precision or simplicity.
Here's how to round to three decimal places:
  • Look at the fourth decimal place. If it's 5 or more, round the third decimal place up by one. If it's less than 5, keep the third decimal place as it is.
  • For our example, 13.527749 becomes 13.528 after rounding, because the fourth decimal place is 7 (which is more than 5).
Rounding makes complex numbers easier to work with while still maintaining a useful level of accuracy.

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