Properties of Surds
The following are the key properties of surds.
- Sum and difference of a rational number and a quadratic surd can not be equal to a quadratic surd. For example, a + b ≠ √c
- If p ± √q = x ± √y , then p = x and q = y
- If √(a+√b) = √c + √d , then √(a-√b) = √c – √d & vice versa.
- Surds cannot be added. For example, √a + √b ≠ √(a+b)
- Surds can not be subtracted. For example, √a – √b ≠ √(a-b)
- Surds can be multiplied. For example, √a × √b = √(a×b)
- Sureds can be divided. For example, √a/√b = √a/√b
What are Surds?
Surd is a mathematical term used to refer square roots of non-perfect squares. For example, √2, √3, √5 are few examples of Surds. It can also include higher roots like cube roots when these cannot be simplified to a rational number.
Surds
In simple terms, Surd is a mathematical term for an irrational number that can be expressed as the root of an integer. Most commonly, surds are used to refer to square roots of non-perfect squares, such as \(\sqrt{2}\), \(\sqrt{3}\), or \(\sqrt{5}\), but they can also include higher roots like cube roots (\(\sqrt[3]{7}\)) when these cannot be simplified to a rational number.
Let’s know more about Surds and it’s types, rules, properties and examples in detail below.
“Surd” is a Latin word which means deaf or mute. In earlier days, Arabian mathematicians identified rational numbers and irrational numbers as audible and inaudible numbers. Surds are irrational numbers, so they were called asamm (deaf) in the Arabic language, and as surds in the Latin language. Surd is an essential topic in mathematics.
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