What is the square root of 28?

The square root of 28 is a mathematical value that, when multiplied by itself, equals 28. In its exact form, it's written as √28, and in decimal form, it equals approximately 5.2915026221. This concept is fundamental in Class 10 mathematics, particularly when studying chapters on real numbers, algebra, and geometry. Understanding square roots is essential because they appear frequently in various mathematical applications, from solving quadratic equations to calculating distances using the Pythagorean theorem.

When we talk about the square root of 28, we're essentially asking: "What number times itself gives us 28?" Unlike perfect squares such as 25 (which equals 5 × 5) or 36 (which equals 6 × 6), the number 28 doesn't have a whole number as its square root. This is because 28 falls between two consecutive perfect squares: 25 and 36. Therefore, we can immediately deduce that √28 must be greater than 5 but less than 6. More precisely, since 28 is closer to 25 than to 36, the square root of 28 will be closer to 5 than to 6.

In practical applications, square roots like √28 appear in numerous real-world scenarios. For instance, if you're designing a square garden with an area of 28 square meters, each side would measure √28 meters. In construction and engineering, these calculations help determine dimensions, materials needed, and structural measurements. In physics, square roots are used in formulas involving velocity, acceleration, and energy calculations. For Class 10 students preparing for board examinations, it's crucial to understand both the conceptual meaning of square roots and the various ways to express them—whether in radical form (√28), simplified radical form (2√7), or decimal approximation (5.29). This versatility in representation allows students to choose the most appropriate form based on the context of the problem they're solving.