Final answer:
To simplify radicals, find the prime factorization of the number under the radical, bring out the square roots of perfect squares, multiply numbers inside and outside the radical, and eliminate terms to simplify the expression.
Step-by-step explanation:
The task at hand is to distribute and simplify the given mathematical expressions, which include operations such as subtraction, addition, division, and radical simplification. While the student presented multiple expressions, without clear separation, we can address the concept of simplifying square roots as part of the answer.
Steps to Simplify Radicals
Identify the radical you need to simplify.
Find the prime factorization of the number under the radical.
Determine if any of the prime factors are perfect squares (like 4, 9, 16, etc.)
Take the square root of perfect squares, and bring them outside the radical sign.
Multiply any numbers outside the radical together.
Multiply any numbers inside the radical together.
Simplify the expression further if needed by eliminating terms or combining like terms.
Check the answer to ensure it is reasonable and simplified as much as possible.