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SURDS, Faraz - Y9B - Coggle Diagram
SURDS
Rules of Surds
A root of a positive real quantity is called a surd if its value cannot he exactly determined. √9, ∛64, ∜(16/81) etc. are rational numbers but not surds because √9 = 3, ∛64 = 4, ∜(16/81) = 2/3 etc.
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The sum and difference of two simple quadratic surds are said to be conjugate surds or complementary surds to each other. Thus, (4√7 + √6) and (4√7 - √6) are surds conjugate to each other.
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To express in the simplest form, denominator must be rationalized.
The method of convening a given surd into a rational number on multiplication by another suitable surd is called rationalization of surds. In this case the multiplying surd is called the rationalizing factor of the given surd and conversely.
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If a + √x = 0, then a = 0 and x = 0.
If a - √x = 0, then a = 0 and x = 0.
Types of Surds
Similar Surd: When surds have the same common factors, they are known as similar surds.
Mixed Surds: When numbers can be expressed as a product of rational and irrational numbers, it is known as a mixed surd.
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Simple Surd: When there is only a number present in the root symbol, then it is known as a simple surd. For example √2 or √5.
Binomial Surd: when two surds give rise to one single surd, the resultant surd is known as binomial surds.
Definition of Surds
Surds are number left in root form to express its exact value, it cannot be simplified into whole or rational numbers.
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