Rational and Irrational Numbers
What are Rational and Irrational Numbers?
A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where p is the numerator and q is the denominator, and q is not equal to zero whereas irrational number is a number that cannot be expressed as the quotient of two integers. In other words, its decimal representation goes on forever without repeating, and it cannot be written as a fraction.
What are some Rational and Irrational Number Examples?
Some rational and irrational number examples are 10 / 2 and √2 respectively.
What are Difference Between Rational and Irrational Numbers?
The main difference between the rational and irrational numbers is that rational numbers can be represented in p/q form and irrational numbers cannot be represented in p/q form.
Can Square Root of a Non-Perfect Square be Rational?
Yes, the square root of a non-perfect square can be rational. For example, √4 is rational because it equals 2. However, the square root of certain non-perfect squares, like √2 or √5, is irrational.
How can you Prove a Number is Irrational?
One common method to prove a number is irrational is proof by contradiction. Assume the number is rational, express it as a fraction, and then derive a contradiction. This contradiction shows that the original assumption of the number being rational must be false.
Are all Square Roots of Integers Irrational?
No, not all square roots of integers are irrational. The square root of a perfect square (e.g., √4, √9, √16) is rational, as it results in a whole number. However, the square root of a non-perfect square (e.g., √2, √5) is typically irrational.
Can an Irrational Number be Raised to a Rational Power to Yield a Rational Result?
Yes, it is possible for an irrational number to be raised to a rational power and yield a rational result. For example, \( (\sqrt{2})^2 = 2 \) is rational.
Can Sum or Product of a Rational and an Irrational Number be Rational?
Yes, it is possible. The sum or product of a rational and an irrational number can be either rational or irrational. It depends on the specific numbers involved.
Rational and Irrational Numbers
Rational numbers and Irrational numbers are real numbers with unlike characteristics. Rational numbers are the numbers which can be represented in the A/B form where B ≠ 0. Irrational numbers are the numbers that cannot be represented in A / B form. In this article, we’ll learn the concepts of rational numbers and irrational numbers and explore the difference between them.
Table of Content
- What is Rational number?
- How to identify rational numbers?
- What are Irrational Numbers?
- How to Identify Irrational Numbers?
- How to Classify Rational and Irrational Numbers?
- Difference Between Rational and Irrational Numbers