In Exercises 33–46, simplify each expression.____√(−4)²

Verified step by step guidance

1. Identify the expression under the square root: \((-4)^2\).
2. Calculate \((-4)^2\) by squaring -4, which is \((-4) \times (-4)\).
3. Recognize that squaring a negative number results in a positive number, so \((-4)^2 = 16\).
4. Substitute the result back into the square root expression: \(\sqrt{16}\).
5. Simplify \(\sqrt{16}\) by finding the principal square root of 16.

Key Concepts

Square Root

The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the expression involves the square root of a squared term, which simplifies to the absolute value of the original number. Understanding how square roots and squares interact is crucial for simplifying expressions correctly.

Absolute Value

Absolute value refers to the non-negative value of a number without regard to its sign. For example, the absolute value of both 4 and -4 is 4. When simplifying expressions involving square roots of squared numbers, recognizing that the result will always be non-negative is essential for accurate simplification.

Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part, typically expressed in the form a + bi, where 'i' is the imaginary unit defined as the square root of -1. In this exercise, understanding that the square root of a negative number involves complex numbers is important for correctly interpreting and simplifying the expression.