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Are decimal numbers integers or rational numbers?
They can be integers, rational numbers or even approximations for irrational numbers.
Can you multiply two irrational numbers to get a rational number?
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.).
Is the square root of -24 rational?
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.
Are there fewer rational numbers than irrational numbers?
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.
Which irrational number is closest to 6?
The irrational number closest to 6 is the square root of 36, which equals 6. This is because the square root of 36 is a rational number that is the closest approximation to 6 among irrational numbers. The square root of 36 is equal to 6, making it the irrational number closest to 6.
