Here are the essential concepts you must grasp in order to answer the question correctly.
Radical Expressions
Radical expressions involve roots, such as square roots, cube roots, etc. In this context, √2 and √7 are square roots of 2 and 7, respectively. Understanding how to manipulate these expressions is crucial for simplifying and performing operations like addition, subtraction, and multiplication.
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Binomial Expansion
The expression (√2 + √7)² is a binomial that can be expanded using the formula (a + b)² = a² + 2ab + b². This formula allows us to systematically calculate the square of a sum, which is essential for simplifying the expression correctly.
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Simplifying Radical Expressions
After expanding the binomial, the next step is to simplify any resulting radical expressions. This involves combining like terms and reducing radicals when possible, such as simplifying √14 or recognizing that √a * √b = √(ab). Mastery of these simplification techniques is key to arriving at the final answer.
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