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No.

The square roots 8 are irrational, as are the square roots of most even numbers.

Q: Are all square roots of even numbers rational?

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They can be integers, rational numbers or even approximations for irrational numbers.

Yes, for example sqrt(2) * sqrt(18) = 6. Note: here sqrt(n) represents the square root (second root) of n. To simplify this expression we obtain: sqrt(2) * sqrt(18) = sqrt(2) * sqrt(2) * sqrt(9) = 2 * 3 = 6. Generally, it is easy to create cases where two or more irrational numbers are multiplied to create a rational number using roots. The definition of the root clearly relates it back to rational numbers. This task becomes more difficult and even impossible if certain combinations of numbers are not allowed (e.g. transcendental numbers, no direct roots, etc.).

No. The square root of -24 isn't even real, let alone rational because the square root of any negative number is going to be an imaginary number.

For any given subset, yes, because there are an infinite number of irrational numbers for each rational number. But for the set of ALL real numbers, both are infinite in number, even though the vast majority of real numbers would be irrational.

Of the "standard sets" -10 belongs to: ℤ⁻ (the negative integers) ℤ (the integers) ℚ⁻ (the negative rational numbers) ℚ (the rational numbers) ℝ⁻ (the negative real numbers) ℝ (the real numbers) ℂ (the complex numbers) (as ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ). Other sets are possible, eg the even numbers.

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It is not closed under taking square (or other even) roots.

Some square roots are rational, some are irrational (and some are not even real).

Every odd or even number is a rational number, and there are a lot more rational numbers besides those.

Every positive number has two square roots, though the roots are not always whole numbers (or even rational numbers). The more obvious of each numbers roots is the positive one.The positive square root of 4 is 2, because 2*2=4.The positive square root of 5 is roughly 2.236068.The other square root of a number is the negative inverse of their positive root. This is because when two negative numbers are multiplied together the negative signs "cancel out", leaving a positive number.The negative square root of 4 is -2, because -2*-2=4.The negative square root of 5 is roughly -2.236068.Zero has only one square root, itself, and no negative number has any (real number) square roots, since no number multiplied by itself will result in a negative.

Hmmmm, tricky question.... seems to me like these numbers would most likely be called..... oh i don't know, numbers maybe?and rational numbers get even easier to answer, because they have true definition.If you are referring to Square (or any) roots, that try using the ______ root of ____.e is Euler's Constant, and Ï€ is pihope this helps-Nick Ogre

They can be integers, rational numbers or even approximations for irrational numbers.

No. In fact, because pi is a transcendental number it cannot be represented in such a way even in a base composed of "ordinary" irrational numbers like square [or other] roots.

There are infinitely many rational numbers between any two rational numbers. And the cardinality of irrational numbers between any two rational numbers is even greater.

You cannot. The diagonal of a unit square cannot be represented by a rational number. However, because rational numbers are infinitely dense, you can get as close to an irrational number as you like even if you cannot get to it. If this approximation is adequate than you are able to represent the real world using rational numbers.

Yes - all numbers that can be written as ratios, even negative numbers, are rational numbers.

Yes, they are numbers in the complex field.Look at it this way: You started to count with positive integers. But with only those numbers subtraction was limited. You could not take 3 from 2. The solution was to introduce negative numbers. That expanded the number system and what you could do with them.You learned to divide, but you could not divide 2 by 3. This time the solution was to introduce [rational] fractions. Again, the number system was expanded as was the range of and its power.You learned about square roots but even common numbers like 2 did not have a square root that was a rational number. So you introduced irrational numbers. Once again, the number system was expanded as was the range of and its power.The next hurdle was the square root of negative numbers. The solution was to introduce complex numbers. And once again ... you guessed!The introduction of each additional set of number comes as you get into more complicated areas of the subject. In the UK you will not come across complex numbers until you study further mathematics at A level.The square roots of -9, for example, are Ã‚Â±3iwhere i denotes the square root of -1.

16 is an even number from 10 to 20, and its square roots are -4 and +4.