What is √28 equal to?

The value √28 is equal to 2√7 in its simplest radical form, or approximately 5.2915026221 when expressed as a decimal. This equivalence demonstrates an important principle in mathematics: the same value can be represented in multiple ways, each useful for different purposes. The radical form 2√7 is considered the "exact" representation because it maintains mathematical precision without any rounding, while the decimal form provides a practical numerical approximation for calculations and measurements.

Understanding that √28 = 2√7 requires knowledge of simplification techniques that are central to Class 10 algebra. The process involves recognizing that 28 can be factored as 4 × 7, where 4 is a perfect square (2²). Since the square root of a product equals the product of the square roots (√(a × b) = √a × √b), we can write √28 = √(4 × 7) = √4 × √7 = 2√7. This simplified form is preferable in mathematical work because it's more concise and often easier to manipulate in algebraic expressions. For example, if you need to multiply √28 by √7, working with 2√7 makes the calculation straightforward: 2√7 × √7 = 2 × 7 = 14.

The relationship between different representations of √28 also illustrates the concept of mathematical equivalence. Whether you write √28, 2√7, or 5.2915..., you're referring to the same mathematical object—the positive number that, when squared, produces 28. In examinations, students should be prepared to work with any of these forms and convert between them as needed. The radical form (2√7) is typically preferred for exact answers, especially when the problem involves other radicals or when subsequent calculations might benefit from keeping the value under the radical sign. The decimal form becomes necessary when you need a numerical estimate for practical applications, such as measuring physical distances, calculating areas, or working with real-world data. Mastering these different representations and knowing when to use each one demonstrates mathematical maturity and prepares students for more advanced mathematics in higher classes.