# Is the product of a rational and rational number rational?

## Is the product of a rational and rational number rational?

The product of a rational number and a rational number is rational. The product of a rational number and an irrational number is irrational.

## Is the product of rational numbers rational?

The product of two rational numbers is rational. We can show why in a similar way: For any two rational numbers and , where are integers, and and are not zero, the product is . Multiplying two integers always results in an integer, so both and are integers, so is a rational number.

What is the product of two rational number is always?

Let pl=x,qm=y. ⇒plqm=xy, where y≠0 and x and y is the lowest term representation which is a rational number. Therefore the product of two rational numbers is always a rational number.

### Why is the sum or product of rational numbers is rational?

So, adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number. “The product of two rational numbers is rational.”

### Is the product of a rational and irrational number always irrational give an example?

Answer Expert Verified The product of a rational and irrational number is irrational. 2 × √5 = 2√5 is an irrational number. ,product of a rational and irrational number always irrational if rational number is not zero.

Why the sum the difference and the product of two rational numbers are rational numbers?

“The sum of two rational numbers is rational.” So, adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number.

#### Can the product of two irrational numbers be rational?

Irrational numbers are the numbers that cannot be represented as a simple fraction. It is a contradiction of rational numbers but is a type of real numbers. Depending on the two numbers, the product of the two irrational numbers can be a rational or irrational number. √3 × √3 = 3 It is a rational number.

#### Is 10 a rational number or irrational?

The number 10 is an irrational number if 10 canNOT be expressed as a ratio, as in irRATIOnal. A quotient is the result you get when you divide one number by another number. For 10 to be an irrational number, the quotient of two integers canNOT equal 10.

What determines if a number is irrational?

In mathematics, an irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers and b is non-zero. Informally, this means that an irrational number cannot be represented as a simple fraction. Irrational numbers are those real numbers that cannot be represented as terminating or repeating decimals.

## What are examples of rational number?

A rational number is either a terminating or non-terminating but recurring (repeating) decimal. A rational number may be positive, negative or zero. Examples: The sum, difference and the product of two rational numbers is always a rational number.

## Are all rational numbers irrational numbers?

Rational numbers are all real numbers, and can be positive or negative. A number that is not rational is called irrational. Most of the numbers that people use in everyday life are rational. These include fractions and integers.