Evaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁴√−16

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots or fourth roots. The notation ⁴√ indicates the fourth root, which asks for a number that, when raised to the fourth power, equals the given value. Understanding how to manipulate and evaluate these expressions is crucial for solving problems involving roots.

Real Numbers

Real numbers include all the rational and irrational numbers that can be found on the number line. However, certain roots, such as the fourth root of a negative number, do not yield real numbers. Recognizing when a root results in a non-real number is essential for correctly evaluating expressions.

Complex Numbers

Complex numbers extend the concept of real numbers to include solutions to equations that do not have real solutions, such as the square root of negative numbers. They are expressed in the form a + bi, where 'a' is the real part and 'bi' is the imaginary part. Understanding complex numbers is necessary when dealing with roots of negative values.