SURDS: Multiplication and Division of Surds_ Lesson Two

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Surds are expressions that involve square roots or other roots that cannot be simplified to rational numbers. They often appear as radicals (√) in equations. For example, √2, √3, √5, etc., are all surds because they cannot be expressed as a finite decimal or fraction.


Here are a few key points about surds:


Irrational Numbers: Surds represent irrational numbers, meaning they cannot be expressed as a fraction of two integers and have non-repeating, non-terminating decimal expansions.


Simplest Form: Surds are usually written in their simplest form, which means that the radical cannot be simplified further. For example, √8 can be simplified to 2√2, but √2 is already in its simplest form.


Operations with Surds: Surds can be added, subtracted, multiplied, and divided just like regular numbers. When adding or subtracting, it's important to ensure the radicals are of the same type (e.g., both square roots or both cube roots). When multiplying or dividing, you multiply or divide the numbers outside the radicals and then separately multiply or divide the numbers inside the radicals.


Rationalizing the Denominator: Sometimes in mathematical expressions, it's desirable to remove surds from the denominator of a fraction. This process is called rationalizing the denominator. For example, if you have 1/√2, you can rationalize the denominator by multiplying both the numerator and denominator by √2 to get √2/2.


Understanding surds is crucial in various areas of mathematics, including algebra, calculus, and geometry, as they frequently appear in equations
and formulas.
   • SURDS_Lesson One