if there is no integer answer, they are irrational
ex. sq root 5 is irrational but sq root 9 = 3 so it is rational,integer, counting number
if you are taking sq root of a negative they are imaginary ex. sqroot (-9)
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The square roots of all positive real numbers are real numbers.
The square roots of all negative real numbers are imaginary numbers.
Some square roots are rational, but the vast majority are irrational.
Only a set can have subsets, a number such as -2.38 cannot have subsets.
The number 1.68 belongs to the subsets of real numbers known as rational numbers and decimal numbers. As a rational number, 1.68 can be expressed as the ratio of two integers (84/50). It is also a decimal number, specifically a terminating decimal, where the digits after the decimal point eventually end.
There are infinitely many subsets of real numbers. For example, {2, sqrt(27), -9.37} is one subset.
The rational numbers are a subset of the real numbers. You might recall that rational numbers are those that can be expressed as the ratio of two whole numbers (no matter how large they are). Irrational numbers, like pi, cannot. But both sets (the rational and irrational numbers) are subsets of the real numbers. In fact, when we look at all the numbers, we are looking at the complex number system. We break that down into the real and the imaginary numbers. And the real numbers have the rational and irrational numbers as subsets. It's just that simple.
An irrational number is a number that can't be expressed by a fraction having integers in both its numerator and denominator. A rational number can be.
Only a set can have subsets, a number such as -2.38 cannot have subsets.
{natural, whole, integers, rational, real}
Integers, Rational numbers, Real numbers and Complex numbers.
The set of real numbers is infinitely large, therefore it has an infinite amount of subsets. For example, {1}, {.2, 4, 800}, and {-32323, 3.14159, 32/3, 6,000,000} are all subsets of the real numbers. There are a few, important, and well studied namedsubsets of the real numbers. These include, but aren't limited to, the set of all prime numbers, square numbers, positive numbers, negative numbers, natural numbers, even numbers, odd numbers, integers, rational numbers, and irrational numbers. For more information on these, and other, specific subsets of the real numbers, follow the link below.
The two main DISJOINT subsets of the Real numbers are the rational numbers and the irrational numbers.
The number 1.68 belongs to the subsets of real numbers known as rational numbers and decimal numbers. As a rational number, 1.68 can be expressed as the ratio of two integers (84/50). It is also a decimal number, specifically a terminating decimal, where the digits after the decimal point eventually end.
Real number set, imaginary number set, and their subsets.
There are infinitely many subsets of real numbers. For example, {2, sqrt(27), -9.37} is one subset.
The subsets of all the square roots of 144 are {+12} and {-12}. The single set that includes all the square roots of 144 is {+12, -12}. That's all there are. There are no more.
All rational numbers are real so the phrase "real rational" has no meaning. There are an infinite number of subsets: The emply or null set, {1,1.5, 7/3}, {2}, (0.1,0.2,0.3,0.66..., 5.142857142857...} are some examples.
Both are subsets of the real numbers.
Rational Numbers and Irrational Numbers