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Q: What is A number whose square roots are integers or quotients of integers?

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It is a perfect square.

Such a number is called a "perfect square".

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It is a perfect square.

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A factor tree has factors, not square roots - unless they are integers.

Large perfect squares.

All integers are square roots. 3 is the square root of 9.

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No. The only square roots of integers that are rational numbers only when the integer is a perfect square.

A perfect square other than 0.

The square roots of 600 are not perfect integers. Rounded to two decimal places, they are equal to Â±24.49.

All of the integers between 20 and 30 are square roots.

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Integers, odd integers, negative integers, odd negative integers, rational numbers, negative rational numbers, real numbers, negative real numbers, square roots of 1, etc.

Only if the integer is a perfect square.

The square roots of 25 are integers, not fractions.

Are you talking about negative powers.

No. A number will have a rational square root, only if both the numerator and denominator of the simplified fraction are squares of integers.

Rational numbers include integers, and any number you can write as a fraction (with integers in the numerator and denominator). Most numbers that include roots (square roots, cubic roots, etc.) are irrational - if you take the square root of any integer except a perfect square, for example, you'll get an irrational number. Expressions involving pi and e are also usuallyirrational.

The square root of any positive square number is always rational as for example the square root of 36 is 6 which is a rational number.

The square root of 200 is not an integer (whole number). In rounded form, the two square roots of 200 are positive and negative 14.14214... .

perfect squares

The square roots of 117 are irrational numbers and so are not two integers - consecutive or otherwise.

Of course they can. Every integer greater than zero is a square root.