What is √28 as a decimal?

The square root of 28 expressed as a decimal is approximately 5.2915026221. This decimal representation provides a numerical value that's practical for calculations, measurements, and real-world applications where an exact radical form isn't necessary. Understanding how to work with decimal approximations of irrational numbers is an important skill for Class 10 students, particularly when solving practical problems in physics, engineering, economics, and everyday life situations that require numerical answers.

The decimal value 5.2915026221 represents an approximation because √28 is an irrational number, meaning its decimal expansion continues infinitely without repeating or terminating. No matter how many decimal places you calculate, you'll never reach an exact representation—the digits continue forever in a non-repeating pattern. This is fundamentally different from rational numbers like 1/4 (which equals 0.25 exactly) or 1/3 (which equals 0.333... with a repeating pattern). The irrational nature of √28 means that any decimal form is necessarily an approximation, though we can make it as accurate as needed by calculating more decimal places. For most practical purposes, rounding to 2-4 decimal places is sufficient: 5.29, 5.292, or 5.2915.

To obtain the decimal value of √28, you can use a scientific calculator by entering 28 and pressing the square root button (√), or you can use the exponential function to calculate 28^(0.5), since taking the square root is equivalent to raising to the power of 1/2. Many calculators and computer programs also allow you to specify the desired precision. When working with decimal approximations in mathematical problems, it's important to maintain consistency in rounding throughout your calculations to minimize cumulative rounding errors. For instance, if you round √28 to 5.29 early in a multi-step calculation, small errors may accumulate, potentially affecting your final answer. A better approach is to keep the value in radical form (2√7) throughout your work and only convert to decimal in the final step if a numerical answer is required.