Which best explains what determines whether a number is irrational? a) a number that can be written as a decimal that repeats and does not terminate b) a number that can be written as a decimal that terminates and does not repeat c) a number that can be written as a square root that does not result in a whole number d) a number that can be writtten as a decimal that neither repeats nor terminates

Irrational number can be written as decimal number that, neither a terminating decimal or repeating decimal. Thus, the option D is the correct option, which is a number that can be written as a decimal that neither repeats nor terminates.

Irrational numbers are the number which is the real number but not the rational number(a/b).The irrational numbers can not be represents in the fractional form.

Irrational numbers are written in the form of root of a number such as,

,   ,     etc.

Irrational number can be written as decimal number that, neither a terminating decimal or repeating decimal.

Lets check all the given options as,

Hence, A number that can be written as a decimal that neither repeats nor terminates the option D is the correct option.

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Option: D is the correct answer.

D) a number that can be written as a decimal that neither repeats nor terminates

We know that real numbers are  divided into two categories:

1)

  Rational Number--

A number that can be expressed in the form of p/q i.e. a fraction where p belongs to integers and q belongs to natural numbers and also the decimals which are terminating and  repeating.

2)

   Irrational Number--

A number that cannot be expressed in the form of p/q are irrational also the non-repeating and non-terminating decimals are considered as irrational.

         Hence, the answer is:

            Option: D

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