Multiply. See Example 7. (√5 + 2)²

Verified step by step guidance

1. Recognize that the expression \((\sqrt{5} + 2)^2\) is a binomial squared, which can be expanded using the formula \((a + b)^2 = a^2 + 2ab + b^2\).
2. Identify \(a = \sqrt{5}\) and \(b = 2\) in the expression.
3. Calculate each term separately: \(a^2 = (\sqrt{5})^2\), \(2ab = 2 \times \sqrt{5} \times 2\), and \(b^2 = 2^2\).
4. Write the expanded form by summing the three terms: \(a^2 + 2ab + b^2\).
5. Simplify each term where possible, such as \((\sqrt{5})^2 = 5\) and \(2^2 = 4\), then combine all terms to express the final expanded form.

Key Concepts

Binomial Expansion

Binomial expansion is a method to expand expressions raised to a power, such as (a + b)². It follows the formula (a + b)² = a² + 2ab + b², allowing you to multiply and simplify the expression without direct multiplication.

Square of a Sum

The square of a sum involves squaring a binomial by applying (a + b)² = a² + 2ab + b². This concept helps in breaking down complex expressions into simpler terms, making it easier to calculate or simplify.

Simplifying Radicals

Simplifying radicals involves reducing square roots to their simplest form or combining like terms involving radicals. This is essential after expansion to write the final answer in a clear and simplified manner.