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Q: Is the length diagonal of a square with side 5 a real number?

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The length of the diagonal of any square whose sides are a whole number of units.

In the simplest case, it is use to find the diagonal length of a unit square.

It has been known from very ancient times that the length of the diagonal of a unit square is not a rational number. There were no specific mathematicians who "discovered" real numbers. Furthermore, all mathematicians of any significance, contributed to our understanding of real numbers.

not in the real world. The area of a square = The length of a side, squared. Any number squared is positive.

The square of a real number is always a real number.

The diagonal of a rectangle does not provide enough information to determine the length of the rectangle. Let L be any real number such that 32/sqrt(2) < L < 32. let B = sqrt(32^2 - L^2) Since L < 32 the above square root exists, and since L > 32/sqrt(2), B < L. So the rectangle with sides of L and B will have a diagonal of 32 inches. But L is any of an infinite number of possible real numbers. Therefore there are infinitely many possible solutions.

The diagonal of a unit square, for example, is radical(2).

I thought it was real... square of -x is the same as the square of +x

Of course, not only can it be a real number but it is a real number. When you take the square root times itself, the result is a number that is real.

The square root of seven is a real number, but it is not a whole number.

It is not the square of a whole number; but it is the square of a real number. If you calculate the square root of 23, you will get a real number. That real number times itself will equal 23. But the square root will not be a simple whole number. It will have an endless decimal fraction.

The square root of 0 is 0, which is a real number.

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