What is the positive square root of 28?

The positive square root of 28 is the same as the square root of 28, which equals 2√7 in simplified radical form or approximately 5.2915026221 in decimal form. The term "positive" is specified because every positive number actually has two square roots: one positive and one negative. For example, both 5 and -5, when squared, equal 25. However, when we use the radical symbol √, we're specifically referring to the principal (positive) square root. This convention is standard in mathematics and is particularly important for Class 10 students to understand when solving equations.

The distinction between positive and negative square roots becomes crucial when solving quadratic equations. Consider the equation x² = 28. This equation has two solutions: x = √28 (the positive square root, approximately 5.29) and x = -√28 (the negative square root, approximately -5.29). Both values, when squared, produce 28 because multiplying two negative numbers yields a positive result: (-5.29) × (-5.29) ≈ 28. However, when we write √28 without any additional notation, we're referring exclusively to the positive value. If we want to indicate both square roots, we write ±√28 (read as "plus or minus the square root of 28").

This concept has practical implications in various mathematical and real-world contexts. In geometry, when calculating the side length of a square with area 28 square units, we use only the positive square root because physical dimensions cannot be negative. Similarly, in physics problems involving distance or time, we typically use only positive square roots since these quantities are inherently positive. However, in pure mathematics, particularly when solving polynomial equations, both positive and negative roots may be valid solutions depending on the context. For Class 10 students, understanding this distinction is essential for correctly interpreting problem statements and providing appropriate solutions. When a question asks for "the square root of 28," you should provide the positive value, but when solving an equation like x² = 28, you should recognize that both x = 2√7 and x = -2√7 are valid solutions. This nuanced understanding reflects a deeper comprehension of mathematical principles beyond mere calculation.