Perform the indicated operations. Assume all variables represent positive real numbers. (√3 + √8)²

Verified step by step guidance

1. Recognize that the expression $(\sqrt{3}+\sqrt{8}{)}^2$ is a binomial squared, which can be expanded using the formula $(a+b{)}^2=a^2+2ab+b^2$.
2. Identify $a=\sqrt{3}$ and $b=\sqrt{8}$ in the expression.
3. Calculate $a^2$ by squaring $\sqrt{3}$, which results in 3.
4. Calculate $b^2$ by squaring $\sqrt{8}$, which results in 8.
5. Calculate $2ab$ by multiplying 2, $\sqrt{3}$, and $\sqrt{8}$, which simplifies to $2\times \sqrt{3}\times \sqrt{8}$.

Key Concepts

Square of a Binomial

The square of a binomial follows the formula (a + b)² = a² + 2ab + b². This means that when squaring a sum of two terms, you must square each term individually, double the product of the two terms, and then combine these results. Understanding this formula is essential for simplifying expressions like (√3 + √8)².

Square Roots

Square roots are the values that, when multiplied by themselves, yield the original number. For example, √3 is a number that, when squared, equals 3. In the context of the given expression, recognizing how to handle square roots is crucial for simplifying the terms √3 and √8 before performing further operations.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable or radical part. In the expression (√3 + √8)², after applying the square of a binomial formula, you will need to simplify the resulting expression by combining any like terms, which is a fundamental skill in algebra for simplifying expressions.