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a square root is not always an irrational number
what is correct? ex: If a square root is not a perfect square, then it is considered an irrational number. These numbers cannot be written as a fraction because the decimal does not end (non-terminating) and does not repeat a pattern (non-repeating)
a fraction is never an irrational number
what is correct? ex: Irrational numbers can't be expressed as a fraction with integer values in the numerator and denominator of the fraction. Irrational numbers don't have repeating decimals. Because of that, there is no definite value of irrational numbers.
a decimal is sometimes an irrational number
what is correct? ex: Any real number that cannot be written in fraction form is an irrational number. These numbers include non-terminating, non-repeating decimals, for example , 0.45445544455544445555..., or . Any square root that is not a perfect root is an irrational number.
a repeating decimal is an irrational number
what is all mixed up? ex:Repeating or recurring decimals are decimal representations of numbers with infinitely repeating digits. Numbers with a repeating pattern of decimals are rational because when you put them into fractional form, both the numerator a and denominator b become non-fractional whole numbers.
a mixed number is not a rational number
what is all mixed up? ex: Mixed numbers are all rational numbers because they can be expressed as a fraction. To be a rational number, a number must be able to be written as a fraction that has an integer as its numerator and a non-zero integer as its denominator.
A rational number is a number that can be written as a fraction a/b where both a and b are integers.
what is correct? ex: Numbers that can be expressed as a/b fraction form is a rational number where a is an integer and b is a non-zero integer. The rational number a/b can also be written as a ratio a:b. Since a and b are integers with b not equal to 0, the given statement is true.
An irrational number is a number that is not rational. This means that it cannot be written as a ratio of integers.
what is correct? ex: A rational number includes any whole number, fraction, or decimal that ends or repeats. An irrational number is any number that cannot be turned into a fraction, so any number that does not fit the definition of a rational number.
the sum of a rational number and a rational number is a rational number
what is correct? ex: a rational number can be expressed as a fraction with integer values in the numerator and denominator (denominator not zero). So, adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form.
every real number is rational
what is all mixed up? ex:If we combine the rational numbers and the irrational numbers, we get real numbers. Hence, all real numbers are not rational numbers because real numbers also contain irrational numbers
every real number is irrational
what is all mixed up? ex: Irrational numbers are those Real numbers that are not Rational. Rational numbers are those Real numbers that can be expressed as a ratio of two Integers, such as . The set of Rational numbers is not empty, therefore some Real numbers are not Irrational.
3.456 is a irrational number
what is all mixed up? ex: a number that can be written as a fraction is rational
3.14 is a rational number
what is correct? ex: 3.14 is a rational number because it is terminating.
7 is a irrational number
what is all mixed up? ex: 7 is a rational number because it can be written in the form of a ratio such as 7/1.
36 is a irrational number
what is all mixed up? ex: The square root of 36 is expressed by √36, where '√' is the radical symbol and 36 is the radical. √36 is equal to 6, which is a rational number
20 is a rational number
what is correct? ex: The number 20 is an integer, and we have a rule relating integers and rational numbers. All integers are rational numbers.
the square root of pie is irrational
what is correct? ex: Because all square roots of irrational numbers are irrational numbers, and pi is irrational
the square root of 25 is irrational
what is all mixed up? ex: Because √25 = 5 and 5 can be written in the form of a fraction 5/1. It proves that √25 is rational.
the square root of 3 is rational
what is all mixed up? ex: it does not terminate or repeat after the decimal point, √3 is an irrational number.
the square root of 100 is rational
what is correct? ex:√100 = 10. The number 10 is a rational number. So, the square root of 100 is a rational number.
the square root of 6 is rational
what is all mixed up? ex: Since 6 is the product of 2 and 3, the square root of 6 is the geometric mean of 2 and 3, and is the product of the square root of 2 and the square root of 3, both of which are irrational algebraic numbers.