Problem 20 - Prealgebra

Question

Use a calculator to find each square root to the nearest tenth. $$\sqrt{250}$$

Step-by-Step Solution

Answer

\(\sqrt{250} \approx 15.8\)

Step 1: Check Rough Estimation

Before using a calculator, estimate the square root of the number to get an initial understanding. Since 250 is between 225 and 256, we know that \(\sqrt{250}\) is between \(\sqrt{225} = 15\) and \(\sqrt{256} = 16\). So, \(\sqrt{250}\) is estimated to be between 15 and 16.

Step 2: Use Calculator for Exact Value

Now, use a calculator to find the square root of 250. By calculating, you find \(\sqrt{250} \approx 15.8114\).

Step 3: Round to the Nearest Tenth

Round the exact value from the calculator, \(15.8114\), to the nearest tenth. Look at the hundredths place which is 1. Since 1 is less than 5, we round down, resulting in \(15.8\).

Key Concepts

Estimation

When you're asked to estimate the square root of a number, it's a bit like taking a quick peek before finding the exact answer. Let's say you want to estimate \(\sqrt{250}\). First, we try to find two perfect square numbers that our number sits between. For 250, those would be 225 and 256 because \(15^2 = 225\) and \(16^2 = 256\). Since 250 is between 225 and 256, we know \(\sqrt{250}\) will be between 15 and 16.
This approach helps you to have a ballpark idea of what to expect from the square root, which will make it easier when using the calculator. Estimation is not meant to give the exact answer but rather to provide a close approximation that guides your thinking and understanding of where the actual value lies.

Rounding Decimals

Rounding decimals is a way to simplify numbers to make them easier to work with, especially when precision beyond a certain point is unnecessary. When you find \(\sqrt{250}\) with a calculator, you might get a number like 15.8114. To round this to the nearest tenth, we focus on the number in the hundredths place, which is the second digit after the decimal point. Here, it is 1.

• If that number is 5 or greater, you round the number in the tenths place up.
• If it’s less than 5, like it is in this case with 1, you leave the number in the tenths place as it is, so 15.8114 becomes 15.8.

This simplified number still closely approximates the true value but is easier to use in further calculations or when conveying results.

Using a Calculator

Calculators are great tools for finding exact numbers, especially when dealing with square roots. To find the square root of a number like 250, you simply enter it into the calculator and use the square root function. Most calculators have a button labeled \(\sqrt{}\) or you'll use a combination of keys to access this function.

• Enter the number 250,
• Press the square root button,
• And you'll see the result, which is approximately 15.8114 for \(\sqrt{250}\).

This process gives you the exact square root, which can then be rounded if needed. By combining estimation with calculator use, you're ensuring better accuracy and understanding of your results.