2015-01-13T21:49:33+05:30

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Square roots of Prime nos are irrational ex square root of 3 (a prime number)
is approx.. 1.73205080757 so prime no do have square roots but are irrational
2015-01-13T22:01:21+05:30

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Prime numbers and other numbers all have square roots.  All real numbers like 1, 2, 3.444444,  5/6 , √5,    9 , 0197 -- have all square roots.  The number has to be a positive number or zero to have a square root.

For some numbers the square root is an integer or a rational number.

For some numbers, square root is irrational.  You cannot write it as p/q like  4/5...

Prime numbers like  2, 7 , 11, 127  all have  square roots, but they are not written as  2.3389484..  as their decimal digits are endless.  So we write them as

√2,  √3 ,  √7,  √127  like that.