How to Simplify Surds (Irrational Square Roots) Definition, Types, Examples & Uses

How to Simplify Surds (Irrational Square Roots)

Subject: Mathematics

Book: Maths Mastery

“Surd” often refers to an irrational root that can’t be simplified to a rational number, like √2 or √7. We can simplify √18 to 3√2 by factoring out perfect squares. To add or subtract surds, they must share the same radicand: for instance, 2√3 + 3√3 = 5√3. Rationalizing denominators (like 1/√3 becoming √3/3) is key to presenting surd answers in standard form. Surd arithmetic underlies advanced algebra, geometry with exact distances, and calculations where approximations can degrade precision. Familiarity ensures you handle irrational values with exactness and clarity.