Find the square of each radical expression. See Example 2.-√19

Verified step by step guidance

1. Identify the expression to be squared: \(-\sqrt{19}\).
2. Recall that squaring a negative number results in a positive number.
3. Apply the property of exponents: \((-\sqrt{19})^2 = (-1)^2 \times (\sqrt{19})^2\).
4. Calculate \((-1)^2\), which equals 1.
5. Calculate \((\sqrt{19})^2\), which equals 19.

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots, cube roots, etc. The square root of a number 'x' is a value that, when multiplied by itself, gives 'x'. In this case, the expression -√19 represents the negative square root of 19, which is a fundamental concept in understanding how to manipulate and simplify radical expressions.

Squaring a Radical

Squaring a radical expression means multiplying the expression by itself. For example, squaring -√19 involves calculating (-√19) * (-√19), which simplifies to 19. This process is essential for solving problems that require finding the square of radical expressions, as it helps eliminate the radical sign.

Properties of Exponents

Understanding the properties of exponents is crucial when dealing with radical expressions. Specifically, the property that states (a^m) * (a^n) = a^(m+n) can be applied when squaring radicals. This concept helps in simplifying expressions and understanding how to manipulate powers and roots effectively.