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Q: Is the square of 32 rational?

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No.

No, because 32 is not a perfect square.

No.

It is irrational.

It is an irrational number

The square root of 32 is an irrational number

is a square a rational symmetry? is a square a rational symmetry?

No. Lots of square roots are not rational. Only the square roots of perfect square numbers are rational. So for example, the square root of 2 is not rational and the square root of 4 is rational.

The square root of 32 isn't rational, so it can't be a fraction.

The square root of a positive integer can ONLY be:* Either an integer, * Or an irrational number. (The proof of this is basically the same as the proof, in high school algebra books, that the square root of 2 is irrational.) Since in this case 32 is not the square of an integer, it therefore follows that its square root is an irrational number.

A perfect square is the square of an integer, for example, 32 = 9. It might also be the square of a rational number, like the square of 1/2, of 2/3, etc.

The square roots are irrational.

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