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Let's assume that p is prime and the square root of p is rational. This means there are (positive) integers a, b such that sqrt(p) = a/b. Therefore: p = (a/b)*(a/b) = (a^2)/(b^2) This shows that a/b already has to be a (positive) integer, so that (a^2)/(b^2) is also one. (If a/b is not an integer, multiplying it by itself wouldn't create one, since no elements would come in that you could cancel the numerator and the denominator with.) So we have shown that (a^2)/(b^2) = (a/b)^2 = p. But this means that p isn't prime, because it has a/b (an integer) as a divisor, so we have a contradiction of the given fact that p is prime. This makes our assumption that sqrt(p) is rational false, and therefore proves that if p is prime, sqrt(p) is irrational.
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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 .
Are all square roots irrational numbers?
No. Square root of 9=3. 3=3/1. Therefore not all square roots are irrational
Will the square root of a prime number be rational or irrational?
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.
What is the square root of 50 turned into fraction?
The square roots of 50 are irrational numbers. You cannot turn irrational numbers into fractions, which are rational numbers.
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
