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Q: Is the square root of x and the square root of NEGATIVE x both rational and irrational?

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They are both rational.

an irrarional number is a number that can't be written as a fraction or whole number. -sqrt(9)=-3 This is a whole number so it isn't irrational, just rational

They are +5 and -5, which are both rational.

No. The square root of 49 is plus or minus 7, both of which are integers. And integers are rational numbers - whether they are positive or negative.

No, they are both rational.

The sum, or difference, of two irrational numbers can be rational, or irrational. For example, if A = square root of 2 and B = square root of 3, both the sum and difference are irrational. If A = (1 + square root of 2), and B = square root of 2, then, while both are irrational, the difference (equal to 1) is rational.

No, no number can be both rational and irrational.

No number can be both rational and irrational. And, at the level that you must be for you to need to ask that question, a number must be either rational or irrational (ie not neither). 0.555555 is rational.

Integers are rational. In the set of real numbers, every number is either rational or irrational; a number can't be both or neither.

No. The square root of 49 is plus or minus 7, both of which are integers. And integers are rational numbers - whether they are positive or negative.

It will be irrational.

No, -3 is a rational number. All fractions are rational along with all decimals that terminate or repeat. (this applies to both positive and negative numbers.)

The square roots of 16 are +4 and -4 . They're both rational numbers.

If it can't be expressed as a fraction then it is an irrational number

Yes. For example, if you multiply the square root of 2 (an irrational number) by itself, the answer is 2 (a rational number). The golden ratio (Phi, approx. 1.618) multiplied by (1/Phi) (both irrational numbers) equals 1 (rational). However, this is not necessarily true for all irrational numbers.

Sometimes it is and sometimes it isn't. The square root of 2 and the square root of 3 are both irrational, as is their product, the square root of 6. The square root of 2 and the square root of 8 are both irrational, but their product, the square root of 16, is rational (in fact, it equals 4).

It doesn't happen. A number cannot be both rational and irrational. It is possible for it to be NEITHER if it is not Real number, i.e. involves the square root of -1, i.e is an imaginary or complex number number.

Yes. It can also be negative in the numerator. Both positive and negative numbers (as well as zero) can be rational numbers. Both positive and negative numbers can be irrational numbers. Both positive and negative numbers (as well as zero) can be integers.

Actually there are more irrational numbers than rational numbers. Most square roots, cubic roots, etc. are irrational (not rational). For example, the square of any positive integer is either an integer or an irrational number. The numbers e and pi are both irrational. Most expressions that involve those numbers are also irrational.

It can't be both at the same time. Irrational means "not rational".

Certainly. Otherwise, there would be a rational number whose square was an irrational number; that is not possible. To show this, let p/q be any rational number, where p and q are integers. Then, the square of p/q is (p^2)/(q^2). Since p^2 and q^2 must both be integers, their quotient is, by definition, a rational number. Thus, the square of every rational number is itself rational.

The number 3 is a rational number (as is any integer).

It is rational.A number cannot be both rational and irrational.

The square roots of 16 are +4 and -4. Both of them are rational numbers.

The product of an irrational number and a rational number, both nonzero, is always irrational