Irrational Numbers - Pre-Algebra

An irrational number is any number that cannot be written as a fraction of whole numbers. The number pi and square roots of non-perfect squares are examples of irrational numbers.

can be written as the fraction . The term is a whole number. The square root of is , also a rational number. , however, is not a perfect square, and its square root, therefore, is irrational.

A rational number is any number that can be expressed as a fraction where both the numerator and denominator are integers. The denominator also cannot be equal to 0. In this set, the irrational number is because the There is no fraction that can be made, it's decimal goes on and on and does not repeat in a pattern. Using the fraction test, we can prove that the following numbers are rational:

An irrational number is any number that can not be expressed as a ratio of integers, i.e. a fraction. Therefore, the only irrational number listed is .

Pi is the only irrational number listed. Irrational numbers are in the form of infinite non-repeating decimals.

A root of an integer is one of two things, an integer or an irrational number. By testing all five on a calculator, only comes up an exact integer - 5. This is the correct choice.

A rational number is any number that can be expressed as a fraction/ratio, with both the numerator and denominator being integers. The one limitation to this definition is that the denominator cannot be equal to .

Using the above definition, we see , and (which is ) cannot be expressed as fractions. These are non-terminating numbers that are not repeating, meaning the decimal has no pattern and constantly changes. When a decimal is non-terminating and constantly changes, it cannot be expressed as a fraction.

is the correct answer because , which can be expressed as , fullfilling our above defintion of a rational number.

The definition of an irrational number is a number which cannot be expressed in a simple fraction, or a number that is not rational.

Using the above definition, we see that is already expressed as a simple fraction.

any number and

. All of these options can be expressed as simple fractions, making them all rational numbers, and the incorrect answers.

cannot be expressed as a simple fraction and is equal to a non-terminating, non-repeating (ever-changing) decimal, begining with

This is an irrational number and our correct answer.

An irrational number is defined as any number that cannot be expressed as a simple fraction or does not have terminating or repeating decimals. Of the answer choices given, the only number that cannot be expressed as a simple fraction or with repeating or terminating decimals is .

Since ,

.

We can determine which is closer by evaluating .

Since , 9 is the closer integer, and it is the correct choice.

The square root of an integer is either an irrational number or an integer. The latter is the case if and only if there is an integer which, when multiplied by itself, or squared, yields the number inside the symbol (the radicand) as the product. Of , only 81 is the square of an integer (9).

An irrational number is one that cannot be written as a fraction. All integers are rational numberes.

Repeating decimals are never irrational, can be eliminated because

.

and are perfect squares making them both integers.

Therefore, the only remaining answer is .

Let's take two irrationals like and multiply them. The answer is which is rational.

But what if we took the product of and . We would get which doesn't have a definite value and can't be expressed as a fraction.

This makes it irrational and therefore, the answer is sometimes irrational, sometimes rational.

Rational numbers are those which can be written as a ratio of two integers, or simply, as a fraction.

The solution of is , which can be written as . Each of the other answers would have a solution with an infinite number of decimal points, and therefore cannot be written as a simple ratio. They are irrational numbers.

An irrational number cannot be represented as the quotient of two integers.

Irrational numbers do not terminate and are not repeat numbers.

Looking at the possible answers,

can be reduced to , therefore it is an integer.

by definition is a quotient of two integers and thus it is not an irrational number.

can be rewritten as and by definition is a quotient of two integers and thus it is not an irrational number.

is a terminated decimal and therefore can be written as a fraction. Thus it is not an irrational number.

is the number for and does not terminate, therefore it is irrational.

The meaning of irrational states that numbers cannot be rewritten as a ratio of integers. Of the following that could be simplified, the only possible choice of irrational numbers is .

The answer is .

All other options are rational because they can be written as either a fraction of integers or just an integer.

To add the numerator, first multiply the denominator to find the least common denominator.

The common denominator is:

Rewrite the fractions.

A rational number can be put in the form , it can be a terminating decimal, or it can be a repeating decimal. is a continual number, therefore it is an irrational number.

An irrational number is any number that cannot be expressed as a ratio of integers.

Therefore, is considered irrational because it cannot be expressed as a ratio of integers.

An irrational number is a number that cannot be expressed as a ratio of integers and cannot be expressed as terminating or repeating decimals.

Therefore, the only answer that follows this definition is .