Determine whether each number is rational, irrational, or...

Determine whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. If a number is irrational, give a decimal approximation to the
nearest thousandth. Use a calculator as necessary. See Examples 4 and 5.
$$
\sqrt{-47}
$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Real versus Non-real Numbers

The real number system includes all the rational and irrational numbers—those that can be found on the number line. When an expression involves operations, such as extracting the square root of a negative number, the result does not fall within the real number system, marking it as non-real.

Imaginary Numbers

Imaginary numbers arise when dealing with the square roots of negative numbers. They are defined using the imaginary unit 'i', where i is the square root of -1. This extension of the real numbers into the complex number system allows for the effective handling of computations involving negative radicands.

Rational and Irrational Numbers

These categories classify real numbers according to whether they can be expressed as a fraction of two integers. Rational numbers have a precise fractional representation, while irrational numbers cannot be accurately written as a ratio of integers and instead have non-terminating, non-repeating decimal expansions.

Please give Ace some feedback