h = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12 \text{ cm}
["# Understanding the Calculation of h = √(13² – 5²): A Clear and Simple Guide", "Mathematics often involves solving expressions that seem complex at first glance—but with the right steps, even advanced equations become manageable. One such example is the expression:", "$$\nh = \sqrt{13^2 - 5^2}\n$$", "Whether you’re a student mastering algebra or simply looking to clarify a key formula, this equation reveals an elegant solution rooted in the Pythagorean theorem. Let’s break it down step by step.", "### Breaking Down the Expression", "Start with the original expression:", "$$\nh = \sqrt{13^2 - 5^2}\n$$", "This formula is commonly seen in right triangle geometry, particularly when finding the height ((h)) of a triangle formed by two sides of lengths 13 cm and 5 cm. According to the Pythagorean theorem, in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Here, though, we subtract — which sets the stage for calculating a difference under the square root.", "### Step-by-Step Calculation", "1. Square the Numbers\n Compute each square separately:\n $$\n 13^2 = 169\n $$\n $$\n 5^2 = 25\n $$", "2. Subtract Under the Square Root\n Subtract the smaller square from the larger:\n $$\n 169 - 25 = 144\n $$", "3. Take the Square Root\n Now apply the square root:\n $$\n h = \sqrt{144} = 12\n $$", "### Final Result", "$$\nh = 12 \ ext{ cm}\n$$", "### Why This Formula Matters", "This calculation is not just a math exercise — it’s fundamental in trigonometry and geometry. For example, if you’re given two legs of a right triangle, this formula quickly gives you the height (or opposite side) without needing to apply the Pythagorean theorem fully.", "Understanding such formulas enhances problem-solving skills in physics, engineering, architecture, and more — fields that rely heavily on precise geometric relationships.", "### Summary", "- h = √(13² – 5²) simplifies to √144\n- √144 = 12, so h = 12 cm\n- This expression reflects a key principle in geometry tied to right triangles\n- Mastering such calculations strengthens foundational math skills for advanced applications", "If you're learning or teaching math, knowing how to simplify radicals and apply algebra to geometric problems opens doors to deeper understanding and practical problem-solving. Keep practicing — every equation brings clarity and confidence!"]
