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Will the square root of a prime number be rational or irrational?
Wiki User
∙ 12y ago
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.
Wiki User
∙ 12y ago
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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.
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.
How can I how that for any prime number p square root of p is an irrational number?
Suppose not. Let p be prime and n = Sqrt[p]. Since p is an integer, if n is rational, then n is also an integer. So we have n.n = p. But since p is prime, only 1 and p divide p. -><- therefore n must not be rational
Is the square root of 19 irrational or rational?
The square root of the prime number 19 is an irrational number
Is the square root of 169 a rational or irrational number?
The square root of 169 is 13 which is a rational and also a Prime number
Is the square root of 121 rational or irrational?
The square root of 121 is 11 which is a rational number and it is also a prime number
Is - square root 17 irrational rational irrational whole irrational rational?
17 is a prime number with no factors other than itself and 1 therefore minus square root of 17 is an irrational number.
Is the square root of 47 a rational number?
'47' is a prime number, so it does not have a rational square root. sqrt(47) = 6.8556546... to 9 d.p. An irrational number which cannot be converted to a quotient; that is made into a fraction. NB The square roots of prime numbers are irrational.
Is the square root of 19 a rational number?
No. 19 is a prime number, and all prime numbers have irrational roots.
Is 11 a rational or irrational number?
It is a rational number and also a prime number
Is the square root of 17 a rational number?
No because the square root of any prime number is irrational inasmuch that it can't be expressed as a fraction.
Is number 2 rational or irrational?
2 is a rational number and it is also a prime number
Is 2 a rational number or irrational?
It is rational. It is a whole number so it cannot be irrational.
What are some math facts about the number 5?
It is an odd number It is a prime number It is a rational number It is an irrational number when square rooted It is V as a Roman numeral
Is the square root of 3 rational?
Root of '3' is NOT rational. It is an IRRATIONAL Number. To 9 d.p. it is sqrt(3) = 1.732050808.... NB THE square roots of prime numbers are irrational , just like 'pi = 3.141592....'. NNB A irrational number, put casually, is a number were the decimals go to inifinty and there is no regular order in the number2.
