Taking square roots on both sides (noting that the square of a real number is non-negative, and the inequality direction is preserved):

Fri, 01 May 2026 10:34:14 +0000

**Understanding the Power of Taking Square Roots on Both Sides: Why It Matters for Real Numbers** If you’ve ever paused while solving an inequality and wondered whether squaring both sides was safe, you’re not alone. The phrase “taking square roots on both sides (noting that the square of a real number is non-negative, and the inequality direction is preserved)” is sparking quiet curiosity among learners and problem-solvers in the U.S. who value precision and logic in math. At its core, this concept reflects a fundamental truth in algebra and number theory: squaring real numbers never produces negative results. Because the square of any real number is always zero or positive, when you square both sides of an inequality, the sign stays intact—unlike when manipulating absolute values or working with complex numbers. This preserves logical relationships, making it a reliable tool in solving equations and inequalities. ### Why This Concept Is Gaining Attention in the US