Problem 78 - Prealgebra

Question

Use a calculator to approximate the square root to the nearest tenth. \(\sqrt{73}\)

Step-by-Step Solution

Answer

The square root of 73 rounded to the nearest tenth is 8.5.

Step 1: Recognize the Task

The task is to find an approximation of the square root of 73 using a calculator, rounding to the nearest tenth.

Step 2: Enter the Number in a Calculator

Turn on your calculator and enter the number 73. Once entered, find the square root button. It is usually denoted by a symbol similar to '√' or sometimes denoted as a function key like 'sqrt().'

Step 3: Calculate the Square Root

Press the square root button after entering 73 to compute the square root. Your calculator will display the result. In this instance, the display should show approximately 8.544.

Step 4: Round to the Nearest Tenth

Look at the number in the hundredths place to round to the nearest tenth. If the hundredths digit is 5 or greater, round up. If it is 4 or less, round down. Here, 8.544 rounds to 8.5 as the number in the hundredths is 4.

Key Concepts

Using a Calculator

Calculating square roots is simplified greatly with the aid of a calculator. Whether you're using a scientific calculator or a simple digital one, the process remains user-friendly. To start, switch on your calculator. You then input your number, in this case, 73. On most calculators, you can find the square root function as a button labeled "√" or it might be tucked away in a function key labeled "sqrt."
Once you've entered 73 and pressed the square root button, the calculator performs the operation for you. The device will show the result, efficiently giving you the square root of 73, which approximates to 8.544. This step saves time and increases accuracy compared to manual calculations.
Remember, the use of calculators in calculating square roots not only helps in accuracy but also allows you to check your work quickly if done manually.

Approximating Square Roots

Sometimes, you might not have a calculator at hand, or you’ll need to estimate. Approximating a square root helps when exact calculation isn't possible or needed. Using number sense, you identify two perfect squares close to your number. For 73, the closest perfect squares are 64 (as 8 squared) and 81 (as 9 squared).
Knowing that 73 falls between these squares, you find it lies closer to 8. Dividing the difference (73 - 64 = 9 and 81 - 73 = 8) helps understand it's slightly past halfway, nudging you towards estimating just over 8.5.
This approach strengthens mathematical reasoning and aids in understanding how square roots relate to whole numbers. It’s a handy technique for quick estimates in tests or real-life situations.

Rounding Numbers

Rounding is a valuable skill, especially when dealing with decimals. Once you have the result from your calculator (for example, 8.544), rounding it to the nearest tenth simplifies and makes it more understandable.
To round to the nearest tenth, look at the hundredths digit. If it's 5 or more, round up; if it's 4 or below, round down. With 8.544, you see that the hundredths digit is 4, leading you to round down, resulting in 8.5.
This practice enhances precision in reporting numbers and can be particularly helpful in settings that prefer simplification, like engineering or financial estimations. It also deepens the understanding of place value in decimal numbers.