Best Answer

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.

Q: Give a proof that square root of n is irrational for every natural number n that is not a perfect square?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

The square root of (any number that isn't a perfect square) is irrational.

Yes. The square root of any whole number that is not a perfect square is irrational.

No because its square root is an irrational number

Because its square root is an irrational number

The square root of any non-perfect square is an irrational number. Since sqrt(1000) = 10 sqrt(10), it is irrational.

Related questions

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.

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.

The square root of (any number that isn't a perfect square) is irrational.

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).

The square root of ANY positive integer is either a whole number, or an irrational number. Only the perfect squares have whole number square roots; all the rest are irrational. 97 is not a perfect square therefore √97 is irrational.

The square root of (any number that isn't a perfect square) is irrational.

The square root of (any number that isn't a perfect square) is irrational.

The square root of (any number that isn't a perfect square) is irrational.

The square root of (any number that isn't a perfect square) is irrational.

Yes. The square root of any whole number that is not a perfect square is irrational.

Yes. The square root of any number that is not a perfect square (like 9 or 36) is irrational.

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.