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Nice question!
The square root of (any number that isn't a perfect square) is irrational.
No Prime number is a perfect square.
So the square root of any prime number is irrational.
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Is the square root of 5 an irrational or a rational number?
A rational number can be expressed as the ratio of two integers (the number one does not count). An irrational number cannot. The square root of 5 cannot be expressed as the quotient of two integers. This assertion is by experience that the square root of a prime number is irrational. There are several methods to prove the irrationality -- look for them elsewhere. For the sake of curiosity, my calculator gives the following result for it: 2.2360679774997896964091736687312762354406183596115257242708972454105209256378048994144144083787822749695081761507737835042532677244470738635863601215334527088667781731918791658112766453226398565805357613504175337850034233924140644420864325390972525926272288762995174024406816117759089094984923713907297288984820886415426898940991316935770197486788844250897541329561831769214999774248015304341150359576683325124988151781394080005624208552435422355561063063428202340933319829339597463522712013417496142026359047379... You can say that it is irrational by looking at the inexact answer.
Is every prime number a rational number?
Yes. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
Is the square root of 15 rational or irrational?
IRRATIONAL sqrt(15) = sqrt(3 x 5) =sqrt(3) X sqrt(5) Since the 'square roots' of prime numbers , '3' & '5' in this case, are irrational , then the square root od '15' is irrational .
How is root 2 irrational?
2 is a prime number and its square root is an irrational number that cannot be expressed as a fraction
Is the number 0.1111 repeats is it irrational?
NO!!!! It can be converted to a rational fraction. Method. Let P 0.6666.... & 10P = 6.6666.... Subtract 9P = 6.0 = 6 P = 6/9 P = 2/3 With Irrational numbers you cannot convert to a fraction. Casually an irrational number is one which goes to infinity, but the digits are not in any regular order. pi = 3.141592654.. is probably the most famous irrational number. Others being the square root (2) = 1.414213562.... and the square roots of prime numbers.
