Irrational Numbers

The product of a non-zero rational number and an irrational number is irrational because a rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction. When you multiply a non-zero rational number by an irrational number, the result cannot be simplified to a fraction, as it retains the non-repeating, non-terminating nature of the irrational number. Therefore, the product remains irrational.

No it is not. It can be written as a fraction, so it cannot be irrational.

The number 5.131133111 is rational because it can be expressed as a fraction of two integers. Specifically, it can be written as 5131133111/1000000000. Since it has a finite decimal representation, it qualifies as a rational number.

14.23 is a rational number because it can be expressed as a fraction of two integers. Specifically, it can be written as 1423/100, where both 1423 and 100 are integers. Rational numbers include all integers, fractions, and terminating or repeating decimals, making 14.23 fall into this category.

No, 798 is not an irrational number; it is a rational number. Rational numbers can be expressed as the quotient of two integers, and 798 can be written as ( \frac{798}{1} ). In contrast, irrational numbers cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal expansions.

The number 3.456 repeating (often written as (3.456\overline{456})) is a rational number because it can be expressed as a fraction. Rational numbers are defined as numbers that can be written in the form ( \frac{a}{b} ), where ( a ) and ( b ) are integers and ( b \neq 0 ). Since 3.456 repeating has a repeating decimal pattern, it fits this definition.

The number 82 is a rational number because it can be expressed as a fraction, specifically ( \frac{82}{1} ). Rational numbers are defined as numbers that can be written as the quotient of two integers, where the denominator is not zero. Since 82 meets this criterion, it is classified as rational.

-16.87 is a rational number because it can be expressed as a fraction of two integers. Specifically, it can be written as -1687/100, where both -1687 and 100 are integers. Rational numbers are defined as numbers that can be represented as a fraction, and -16.87 meets that criterion.

The number 0.8 can be expressed as a fraction, specifically ( \frac{8}{10} ) or ( \frac{4}{5} ), which shows that it is a rational number. Rational numbers are those that can be written in the form of a fraction ( \frac{a}{b} ), where ( a ) and ( b ) are integers and ( b \neq 0 ). Since 0.8 can be represented as such a fraction, it is not an irrational number.

Pi (π) is an irrational number, meaning it cannot be expressed as a fraction of two integers. When pi is divided by any non-zero integer, such as 26, the result remains irrational. Therefore, π/26 is also irrational.

Any irrational number multiplied by 0.4 will produce an irrational number. For example, if you take the irrational number √2 and multiply it by 0.4, the result, 0.4√2, will also be irrational. Thus, any irrational number you choose will suffice.

0.39 is a rational number because it can be expressed as a fraction of two integers. Specifically, it can be written as 39/100, where both 39 and 100 are integers. Since rational numbers are defined as numbers that can be expressed in this way, 0.39 qualifies as rational.

Any irrational number multiplied by 0.5 will produce another irrational number. For example, if you take the irrational number √2 and multiply it by 0.5, you get 0.5√2, which is also irrational. Thus, any irrational number, when multiplied by 0.5, will result in an irrational number.

25 squared is 625, which is a rational number. Rational numbers are defined as numbers that can be expressed as the quotient of two integers, and since 625 can be represented as 625/1, it falls into this category.

No, 8 squared is not an irrational number. When you square 8, you get 64, which is a whole number and therefore a rational number. Rational numbers can be expressed as the quotient of two integers, and since 64 can be expressed as 64/1, it fits this definition.

Covert refers to actions or processes that are hidden or not immediately observable, while overt refers to those that are visible and evident. Conscious actions are those performed with awareness, whereas unconscious actions occur without awareness. Simple actions are straightforward and uncomplicated, while rational actions are based on logic and reason; conversely, irrational actions lack logical justification. Voluntary actions are made with intention and choice, while involuntary actions happen without conscious control; "couple" typically refers to two individuals in a relationship or partnership.

Yes, the square root of 77 is an irrational number. This is because 77 is not a perfect square, meaning it cannot be expressed as the square of a whole number. Therefore, its square root cannot be written as a simple fraction, which is the defining characteristic of irrational numbers.

Multiplying 8 by any irrational number will produce an irrational number. For example, if you multiply 8 by the square root of 2 (approximately 1.414), the result, 8√2, is irrational. In general, the product of a rational number (like 8) and an irrational number is always irrational.

No, 7.73 is not an irrational number; it is a rational number. Rational numbers can be expressed as the quotient of two integers, and 7.73 can be written as 773/100. In contrast, irrational numbers cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal expansions.

The quotient of a nonzero rational number and an irrational number is always an irrational number. This is because dividing a rational number (which can be expressed as a fraction of integers) by an irrational number cannot result in a fraction that can be simplified to a rational form. Therefore, the result remains outside the realm of rational numbers.

The fraction ( \frac{5}{3} ) is rational because it can be expressed as the ratio of two integers, where the numerator is 5 and the denominator is 3. Rational numbers are defined as numbers that can be written in the form ( \frac{a}{b} ) where ( a ) and ( b ) are integers and ( b ) is not zero. Since both 5 and 3 are integers and 3 is not zero, ( \frac{5}{3} ) is a rational number.

Negative 1.125 is a rational number because it can be expressed as a fraction. Specifically, it can be written as -9/8, which consists of an integer numerator and a non-zero integer denominator. Therefore, since it can be represented in this form, it is classified as rational.

3.14159 is an irrational number because it cannot be expressed as a fraction of two integers. It is a non-repeating, non-terminating decimal, which is characteristic of irrational numbers. In fact, 3.14159 is a rounded approximation of the mathematical constant π (pi), which is also irrational.

0.1875 is a rational number because it can be expressed as a fraction. Specifically, it can be written as 1875/10000, which simplifies to 3/16. Rational numbers are defined as numbers that can be represented as the quotient of two integers, and since 0.1875 meets this criterion, it is considered rational.

No, 0.3754152 is not an irrational number; it is a rational number. Rational numbers can be expressed as a fraction of two integers, and since 0.3754152 can be represented as 3754152/10000000, it qualifies as rational. Irrational numbers, on the other hand, cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal expansions.