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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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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
How many irrational numbers are there between 1 and 6?
There are an infinite number of irrational numbers between 1 and 6. There are all the square roots from 1 to 36 except for 1, 4, 9, 16, 25, and 36. There are all the cube roots between 1 and 216 except for 1, 8, 27, 64, 125, 216. You can calculate fourth roots, fifth roots and continue calculating roots all year long. You should only have your supercomputer calculate irrational roots. Otherwise, you will duplicate. When you have calculated all roots of all prime numbers that fall between one and six, and added in all physical constants, then you will know the answer.
Is the square root of 19 a rational number?
No. 19 is a prime number, and all prime numbers have irrational roots.
Why are the square roots of prime numbers greater than one always rational?
They aren't. The square roots of prime numbers are always irrational.
Is the square root of 68 irrational or rational?
The square roots are irrational.
The square root of 50 is it rational or irrational?
The square roots of 50 are irrational.
Is the square root of 163 rational or irrational?
The square roots of 163 are irrational.
The square root of 84 is it rational or irrational?
The square roots of 84 are irrational.
Can square roots be irrational?
Yes
Are all square roots irrational?
No.
Are all square roots irrational numbers?
No. Square root of 9=3. 3=3/1. Therefore not all square roots are irrational
Is The square root of 0.151 rational or irrational?
The square roots are irrational.
Are all square roots are irrational numbers?
No. The square roots of perfect squares are rational.
Is the square root of three irrational or rational?
The square roots of three are examples of irrational numbers.
