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Chapter 8: Problem 73

Use a calculator to approximate the square root to three decimal places. $$\sqrt{0.56}$$

Short Answer

Expert verified
0.748

Step by step solution

01

- Understand the Problem

We need to approximate the square root of 0.56 to three decimal places using a calculator.
02

- Input into Calculator

Turn on your calculator. Enter the number 0.56, and then press the square root function (usually represented as \(\backslash sqrt{}\)).
03

- Read the Result

After pressing the square root function, the calculator will display the result. Make sure to round the answer to three decimal places.
04

- Approximation

The calculator should approximate the square root of 0.56 as 0.748.

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Key Concepts

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

square roots
A square root is a number that, when multiplied by itself, gives the original number. For example, the square root of 4 is 2 because 2 multiplied by 2 equals 4. Finding the square root of a number that isn't a perfect square, such as 0.56, often requires an approximation. This is because such square roots are usually irrational numbers (numbers that cannot be expressed as a simple fraction) and have non-terminating, non-repeating decimal points.
calculator usage
Using a calculator to find the square root is straightforward. Most calculators have a square root function. It is often represented by the symbol \( \sqrt{} \) or a similar notation. Here are the steps to use the square root function on a calculator:
  • Turn on the calculator.
  • Enter the number whose square root you want to find; in this case, 0.56.
  • Press the square root button.
The display will show the approximation of the square root.
decimal approximation
Decimal approximation means finding a decimal number close to the exact value of the square root. Many real-world applications don鈥檛 need the exact value but an approximation that is good enough for practical use. For instance, the exact value of \( \sqrt{0.56} \) is around 0.748331477354788..., but for most purposes, an approximation of 0.748 is sufficiently accurate. By using a calculator, we can get a quick and precise decimal approximation up to as many places as desired.
rounding numbers
Rounding numbers is reducing the number of digits right after the decimal point based on certain rules for practical use. To round off a number to three decimal places, you look at the fourth digit after the decimal point. If this digit is 5 or more, round up the third digit by one. If it is less than 5, retain the third digit as is. For the square root of 0.56, which approximates to 0.748331477354788, the third decimal place is 8. The fourth place is 3, which is less than 5, so the rounded number remains 0.748.

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