Problem 82 - Prealgebra

Question

Use a calculator to approximate the square root to the nearest tenth. \(\sqrt{223}\)

Step-by-Step Solution

Answer

The approximate square root of 223 is 14.9.

Step 1: Understand the Problem

We need to find the square root of 223 and round the answer to the nearest tenth. This means we will use a calculator to compute \( \sqrt{223} \) and then round off the result.

Step 2: Use Calculator to Find the Square Root

Input \( \sqrt{223} \) into a calculator. The calculator should give you a decimal number representing the square root of 223.

Step 3: Round to the Nearest Tenth

Suppose the calculator gives us \( \sqrt{223} \approx 14.933 \). To round to the nearest tenth, we look at the tenths and hundredths place. Here, the tenths place is 9, and the hundredths place is 3. Since 3 is less than 5, we do not increase the tenths place. So, we round to 14.9.

Key Concepts

Calculator Use

To find the square root of a number like 223, a calculator is a helpful tool. Calculators are designed to handle complex calculations at the press of a button. You simply enter the number and then select the square root function, usually represented by a radical symbol (√). Once you press enter, the calculator quickly computes the square root and displays the result. This number will often be a decimal, providing a precise approximation. The advantage of using a calculator is that it saves time and minimizes errors in manual calculations. It's important to know how to access and use these functions, as they are essential for many mathematical problems involving roots.

Rounding Numbers

Rounding is a crucial skill in estimating and simplifying numbers. When you round to the nearest tenth, you focus on the first decimal place. After finding a decimal representation using a calculator, like 14.933 for \( \sqrt{223} \), check the number in the hundredths place (second decimal digit).

• If this number is 5 or greater, you increase the tenths place by one.
• If the number is less than 5, you leave the tenths place as is.

In our example, since the number in the hundredths place is 3, which is less than 5, you don't round up the tenths place. Thus, 14.933 becomes 14.9 when rounded to the nearest tenth. Rounding helps in making numbers easier to work with while retaining essential information.

Decimals

Decimals represent fractions of a whole and are vital for expressing roots and precise measurements. They are composed of a period (known as a decimal point) followed by digits. Each digit after the decimal point represents a power of ten. For instance, in the decimal 14.933, the 9 is in the tenths place, the 3 is in the hundredths place, and the last 3 is in the thousandths place. Understanding decimals is important because they allow finer accuracy compared to whole numbers. Decimals are particularly useful in cases where exact values are needed, such as in scientific calculations, accounting, or when approximating square roots. When you get a result like 14.933, each decimal place provides more detail about the exact size of the number.