Surd form意思

"Surd form" or "surd" in mathematics refers to irrational numbers that involve roots of integers (radicals) that are not perfect squares. In other words, they are numbers that cannot be expressed as a ratio of integers (they are not rational numbers) and include numbers like √2, √3, π, and e. The term "surd" comes from the Latin word "surdus," which means "unclear" or "unintelligible."

For example, the number √2 is in surd form because it is an irrational number (it cannot be expressed as a fraction) and it involves a root of an integer that is not a perfect square. In contrast, the number √4 (which is equal to 2) is not in surd form because it is a perfect square and can be expressed as a rational number.

When working with surds, mathematicians often use techniques to rationalize expressions or to simplify surd forms. For instance, you might see expressions like (√2 + √3)², which can be simplified to (2√6 + 2) using the distributive property. However, the result still contains a surd because √6 is an irrational number.