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What is a a surd?

Updated: 4/28/2022
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14y ago

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A surd is when an irrational number (a non square number under a square root sign) is simplified for accuracy and ease of legibility.

E.G:

√5 x √2 = √10

There are no such rational numbers as Square root of five or two so when we multiply them (as shown in the exampke above) we show the answer in surd form for simplicity, accuracy and legibility.

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14y ago
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9y ago

When we can't simplify a number to remove a square root (or cube root etc) then it is a surd. Example: √2 (square root of 2) can't be simplified further so it is a surd.

"Surd" used to be another name for "Irrational", but it is now used for a root that is irrational.

Around 820 AD al-Khwarizmi (the guy whom we get the name "Algorithm" from) called Irrational Numbers "'inaudible" ... this was later translated to the Latin surdus ("deaf" or "mute")

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9y ago

A surd is an irrational root of a rational polynomial equation.

A rational polynomial equation is of the form

a(n)*x^n + a(n-1)*x^((n-1) + ... + a(1)*x + a(0) = 0

where the a(k) are rational constants.

A root of that polynomial is a value of x for which the equation is true.


The roots may be rational, irrational or complex numbers (in conjugate pairs).


So 2+ sqrt(3) or

7.3 + sqrt(2 + cuberoot(5.9)) are surds.


However, transcendental numbers, such as pi or e, while irrational, are not solutions to polynomial equations and so are not surds.

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9y ago

A surd is an irrational nth root of a positive integer or a sum of such.

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