Rules about Operations with Rational and Irrational Numbers

Front

What is a rational number?

Back

A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero.

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a simple fraction or ratio of two integers.

Front

What is the result of adding two rational numbers?

Back

The sum of two rational numbers is always a rational number.

Front

What is the result of adding a rational number and an irrational number?

Back

The sum of a rational number and an irrational number is always an irrational number.

Front

What is the result of multiplying two irrational numbers?

Back

The product of two irrational numbers can be either rational or irrational.

Front

What is the result of multiplying a rational number by an irrational number?

Back

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

Front

What is the result of squaring an irrational number?

Back

The square of an irrational number is generally irrational, but there are exceptions (e.g., √2 * √2 = 2, which is rational).

Front

Is the square root of a prime number rational or irrational?

Back

The square root of a prime number is irrational.

Front

What is the result of adding two irrational numbers?

Back

The sum of two irrational numbers can be either rational or irrational.

Front

What is the result of subtracting a rational number from an irrational number?

Back

The result is always an irrational number.