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Chapter 9: Problem 26

Use a calculator to approximate to three decimal places. $$ \sqrt{123} $$

Short Answer

Expert verified
The square root of 123 approximates to 11.091.

Step by step solution

01

- Identify the Expression

The problem asks for the square root of 123, represented as \(\backslash\text\backslash\text\backslashsqrt\backslash\text\backslash\text{123}\).
02

- Use a Calculator

Turn on the calculator and ensure it is in standard mode. Input the value 123.
03

- Calculate the Square Root

Press the square root function key (鈭�) on the calculator. The calculator will display the approximated value of \(\root 123 \).
04

- Approximate to Three Decimal Places

Round the calculated value to three decimal places for the final answer. The numerical value should appear as approximately 11.091.

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Key Concepts

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

Square Root Calculation
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, since 3 times 3 equals 9. To find the square root of any number using a calculator, you need to identify the number first.
In our example, we are tasked with finding the square root of 123.
Here鈥檚 a simple guide:
  • Ensure the calculator is on and in standard mode.
  • Enter the number (in this case, 123) into the calculator.
  • Press the square root (鈭�) button.
    • The calculator will then display the square root of 123.


It's important to remember that the square root of non-perfect squares like 123 will be an irrational number, meaning it cannot be expressed exactly as a fraction and has an infinite number of decimal places.
Decimal Approximation
When dealing with irrational numbers, such as the square root of 123, the decimal result continues infinitely without repeating. Calculators provide a practical solution by approximating these numbers.
In our example, after using the square root function, the calculator shows a decimal approximation of the value.
In practical terms, we often round these approximations to a manageable number of decimal places. Here, you are instructed to approximate to three decimal places. If the calculator provides a longer decimal, you would:
  • Look at the fourth decimal place.
  • If that number is 5 or higher, round the third decimal place up by 1.
  • If it's lower than 5, leave the third decimal place as is.
Using this method, the square root of 123 approximates to 11.091 when rounded to three decimal places.
Using a Calculator
Calculators are powerful tools for performing arithmetic operations and complex calculations. To calculate the square root of a number:
  • First, ensure your calculator is turned on and properly functioning.
  • Make sure the calculator is in the correct mode for basic operations.
  • Input the number whose square root you need to find (in this exercise, 123).
  • Press the square root (鈭�) button.
After following these steps, the calculator will display the result.
For an accurate solution, ensure you understand how to use any additional functions your calculator may have. Many calculators also have a function key that allows for easy rounding of decimals to the desired place.

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