Question

Give three examples that satisfy the given conditions.

A real number that is not a rational number
a) √2
b) 0.5
c) -3
d) 1/3"

Answer 1

Examples of real numbers that are not rational include √2, π (pi), and e (Euler's number). Rational numbers can be written as fractions with integer numerators and denominators, which is not possible for these examples.

Step-by-step explanation:

The question asks for examples of real numbers that are not rational numbers. A rational number can be expressed as the quotient or fraction ⅟, where p and q are integers and q is not zero. Here are three examples that satisfy the given conditions:

• √2 is an irrational number because it cannot be expressed as a fraction of two integers.
• π (pi) is another example of an irrational number as it is a non-terminating, non-repeating decimal.
• e (Euler's number) is also an irrational number, known for its use in natural logarithms and exponential functions.

Options b) 0.5 and d) 1/3 are rational numbers because they can be written as fractions with integers in the numerator and denominator. Option c) -3, although an integer, is also a rational number because it can be expressed as -3/1.