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Give a proof that square root of n is irrational for every natural number n that is not a perfect square?
Let's suppose the opposite and say that it is rational, so we can write it as a fraction of two natural numbers, where m <> 1:
l/m
Let's chose l and m in the way that the fraction l/m will be reduced, i.e, l and m have no common divider.
So, according to the supposed, (l/m)2 = n
From here, l2 = nm2
Now we see that l should be dividible by m. But we've chosen l and m in such a way that it couldn't be. Contradiction.
So we cannot represent the square of n as a rational fracture.
What else can I help you with?
Is the square root 60 irrational?
The square root of (any number that isn't a perfect square) is irrational.
Is the square root of 82 irrational?
Yes. The square root of any whole number that is not a perfect square is irrational.
Why 12348 is not a perfect square?
Because its square root is an irrational number
Is 1700 a perfect square?
No because its square root is an irrational number
Why is the square root of 1000 an irrational number?
The square root of any non-perfect square is an irrational number. Since sqrt(1000) = 10 sqrt(10), it is 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 are the examples of irrational numbers?
The square root of any number which is not a perfect square;The cube root of any number which is not a perfect cube;Pi, the circular constant.e, the natural logarithm base number.
Is the square root 60 irrational?
The square root of (any number that isn't a perfect square) is irrational.
Is the square root of a positive number an irrational number?
Sometimes the square root of a positive number can be irrational, as in the square root of 2 (which is a non-perfect square number), but sometimes it is a rational number, as in the square root of 25 (which is a perfect square number).
Is the square root of 2 irrational or rational?
The square root of (any number that isn't a perfect square) is irrational.
Is the square root of 75 rational or irrational?
The square root of (any number that isn't a perfect square) is irrational.
Is the square root of 30 rational or irrational?
The square root of (any number that isn't a perfect square) is irrational.
Is the square root of 82 irrational?
Yes. The square root of any whole number that is not a perfect square is irrational.
Is the square root of 102 rational of irrational?
The square root of (any number that isn't a perfect square) is irrational.
Is the square root of ten an irrational number?
Yes. The square root of any number that is not a perfect square (like 9 or 36) is irrational.
Is 6 square root of 26 rational number?
It is irrational. * The square root of any positive integer, except of a perfect square, is irrational. * The product of an irrational number and a rational number (except zero) is irrational.
Why 12348 is not a perfect square?
Because its square root is an irrational number
