Find the square of each radical expression. See Example 2. √3x² + 4

Verified step by step guidance

1. Identify the expression that needs to be squared: $\sqrt{3x^2+4}$.
2. Recall that squaring a square root eliminates the square root: $(\sqrt{a}{)}^2=a$.
3. Apply this property to the given expression: $(\sqrt{3x^2+4}{)}^2=3x^2+4$.
4. Simplify the expression if possible. In this case, $3x^2+4$ is already simplified.
5. Conclude that the square of the radical expression $\sqrt{3x^2+4}$ is $3x^2+4$.

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots, cube roots, etc. In the expression √3x² + 4, the term √3x² represents the square root of the product of 3 and the square of x. Understanding how to manipulate and simplify these expressions is crucial for further operations, such as squaring them.

Squaring a Binomial

Squaring a binomial involves applying the formula (a + b)² = a² + 2ab + b². In the context of the given expression, squaring √3x² + 4 requires recognizing it as a binomial and applying this formula to find the square of each term and the cross-product term. This concept is fundamental in algebra and trigonometry for simplifying expressions.

Properties of Exponents

Properties of exponents govern how to handle powers and roots in mathematical expressions. For instance, when squaring a term like √3x², we can use the property that (√a)² = a. This understanding is essential for correctly simplifying the squared radical expression and ensuring accurate calculations in trigonometric contexts.