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Chapter 9: Problem 23

Use a calculator to approximate to three decimal places. $$ \sqrt{75} $$

Short Answer

Expert verified
The approximate value of \(\backslashsqrt{75}\) is 8.660.

Step by step solution

01

Understand the Problem

The task is to approximate the square root of 75 to three decimal places. The symbol for square root is \(\backslashsqrt{...}\).
02

Use a Calculator

Enter \(\backslashsqrt{75}\) into a calculator. Most scientific calculators have a square root function which can be used to find this value.
03

Round to Three Decimal Places

Look at the calculated value of \(\backslashsqrt{75}\) and round it to three decimal places. The rounding rule is to look at the fourth decimal place to see if it is 5 or higher to round up, or less than 5 to keep the third decimal place the same.

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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 is a fundamental mathematical operation. 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, because 3 multiplied by 3 equals 9.
In mathematical notation, the square root of a number x is written as \(\backslashsqrt{x}\).
The task here is to approximate the square root of 75.
Calculator Usage
Using a calculator to find the square root is a fast and efficient method. Most scientific calculators come with a square root function, which is often denoted as \(\backslashsqrt{}\).
Here are the steps to use a calculator for this purpose:
  • Turn on the calculator.
  • Locate the square root button. It might be on the front of the calculator or as a secondary function on one of the keys.
  • Enter the number for which you need the square root. In this case, type in 75.
  • Press the square root button to see the result.
Once you follow these steps, the calculator should display an approximation of \(\backslashsqrt{75}\). The result will be a long decimal number.
Rounding Decimals
Rounding decimals is an important skill, especially in approximations. To round to three decimal places, follow these steps:
  • Identify the fourth decimal place in your number.
  • If the fourth decimal place is 5 or higher, round the third decimal place up by one.
  • If the fourth decimal place is less than 5, keep the third decimal place the same.
For example, if the calculator displays \(\backslashsqrt{75} = 8.660254\), the value rounded to three decimal places would be 8.660 because the fourth decimal place (2) is less than 5.
This method helps ensure your approximations are accurate and consistent.

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