How to solve √100

The square root of 100 (√100) equals 10 because 10 × 10 = 100. This is a perfect square, meaning the square root is a whole number without any decimal or fractional component, making it one of the most straightforward square root calculations.

To solve √100 without memorization, you can list perfect squares: 1² = 1, 2² = 4, 3² = 9, continuing up to 10² = 100, confirming that 10 is the answer. Alternatively, you might recognize that 100 = 10², so applying the property that √(a²) = a gives √(10²) = 10 directly. In contexts requiring both positive and negative roots, the complete solution is ±10 since (-10) × (-10) also equals 100, though in most practical applications, √100 refers specifically to the principal (positive) root of 10. Understanding perfect squares up through at least 20² = 400 enables quick mental calculation for common square root problems and provides reference points for estimating non-perfect squares—for instance, knowing √100 = 10 helps estimate that √105 is slightly more than 10. These skills apply across mathematics, from geometry (calculating side lengths) to algebra (solving quadratic equations) to physics (working with inverse square laws).