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What are all the square roots that are rational?

Many square roots of numbers turn out to be irrational roots, that is irrational numbers . Prime Factors can help determine if a number will have a square root that is rational or irrational. A rational number, is a number that can always be written as a fraction/quotient of integers.

What exactly is a rational root?

Rational root theorem, also called rational root test, in algebra, theorem that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the highest power) must be divisible by the denominator of the fraction and the constant term (the one ...

Are square roots of positive integers rational?

The square root of a positive integer is either a positive integer or an irrational number, but never a non-integral rational number. Proof. Take the set of all positive integers Z + {displaystyle mathbb {Z} ^{+}} and square all its members, label the resulting set Q {displaystyle {mathcal {Q}}} .

Are negative square roots rational or irrational?

Yes. The negative of a rational (i.e. -1 times a positive rational number) is rational. Fractions involving negative numbers, for example -4/7 or 8/(-17) are rational. On the other hand, the negative square root of 2 (= -√2) is irrational.

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