Q: What do you call a number that has integers as its square roots?

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You call them principal square roots.

A square root is the number that is squared to obtain a square number so it can therefore be considered a root of that square number (or basis for that square number). It can also be noted that each square number, when displayed using dots will always form a perfect square perhaps giving it it's name e.g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . etc...

Any positive number x has two square roots: one positive and one negative. For example, +3 and -3 are both square roots of 9. Using a brilliant leap of imagination, mathematicians decided to call the first of these the positive root!

The square of the number

A square number

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Are you talking about negative powers.

a perfect square

You call them principal square roots.

A square root is the number that is squared to obtain a square number so it can therefore be considered a root of that square number (or basis for that square number). It can also be noted that each square number, when displayed using dots will always form a perfect square perhaps giving it it's name e.g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . etc...

Finding the square root. Remember, though that there are two square roots for every positive number the square roots of 9 are 3 and -3 because 3 * 3 = 9 and -3 * -3 = +9

Any positive number x has two square roots: one positive and one negative. For example, +3 and -3 are both square roots of 9. Using a brilliant leap of imagination, mathematicians decided to call the first of these the positive root!

The square of the number

The integers that are usually considered neither prime nor composite are 0 and 1 (and -1 among the negative integers). The number 1 can be described as unity or identity.

a perfect square

Square number.

A square number

I would call an odd number factor a factor that is an odd number. I would call a number with an odd number of factors a perfect square.