Which numbers are irrational? Select all that apply.
To determine which numbers are irrational, it is important to understand the definition of irrational numbers. An irrational number is a real number that cannot be expressed as a simple fraction or ratio of two integers. Instead, they are numbers that go on infinitely without repeating.
Here are some commonly known irrational numbers:
1. π (pi): The ratio of a circle's circumference to its diameter.
2. √2 (square root of 2): The length of the diagonal of a square with sides of length 1.
3. √3 (square root of 3): The length of the diagonal of an equilateral triangle with sides of length 1.
Other examples of irrational numbers include the Euler's number (e), the golden ratio (φ), and the square root of any non-perfect square number.
In summary, the correct answer would be:
- π (pi)
- √2 (square root of 2)
- √3 (square root of 3)