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Sqrt(4) is not a surd, because sqrt(4) is + or - 2, which is rational. On the other hand, sqrt(2) is a surd, and that's because the square root of two is irrational.
A surd is a number that cannot be changed into a fraction. They go on infinitely without any pattern.
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Is every irrational a surd?
Normally they are.
What is an infinite surd?
Infinite surd is a term used in mathematics. The definition of an infinite surd is a never ending irrational number with an exact value that would be left in square root form.
Why was an irrational number called a 'surd' as opposed to an 'irrat'?
The term surd traces back to al-Khwārizmī, who referred to rational and irrational numbers as audible and inaudible, respectively. This later led to the Arabic word "أصم‎" (asamm, meaning "deaf" or "dumb") for irrational number being translated into Latin as "surdus" (meaning "deaf" or "mute").
Is the sum of irrational roots irrational?
Not always. For example: sqrt(2)+(-sqrt(2))=0 which is not irrational.
The square root of 50 is it rational or irrational?
The square roots of 50 are irrational.
