R = \sqrt{a^2 + b^2} = \sqrt{5^2 + 3^2} = \sqrt{25 + 9} = \sqrt{34}

Sun, 03 May 2026 08:39:33 +0000

Understanding the Pythagorean Theorem: How R = √(a² + b²) Powers Geometry and Real-World Calculations When we first learn about right triangles, one formula stands out above the rest: R = √(a² + b²) This deceptively simple equation defines the hypotenuse of a right-angled triangle in terms of its two legs, often denoted as a and b. Whether you're a student mastering geometry or a professional in engineering and architecture, understanding this formula is essential. In this article, we’ll break down how R = √(a² + b²) works, explore a practical example using R = √(5² + 3²), and see why this mathematical principle remains foundational in modern science and daily life. --- ### What Is R = √(a² + b²)?