Simplifying Radicals: Key Concepts and Techniques

What is the term used to describe the number outside the radical that indicates the type of root?

• Exponent

• Radicand

• Index

• Coefficient

What must a radicand not contain to be considered in its simplest form?

• An index

• Perfect square factors other than one

• Variables

• Any numbers

What does the square root of a perfect square result in?

• An irrational number

• A radical expression

• A whole number

• A fraction

Which method involves breaking down the radicand into perfect square factors?

• Perfect squares method

• Square root extraction method

• Factor pairs method

• Radicand division method

What is the simplified form of the square root of 72 using the perfect squares method?

• 6√2

• 8√3

• 3√8

• 9√2

In the factor pairs method, what is the purpose of finding pairs of factors?

• To find the index

• To identify the radicand

• To simplify the expression by taking square roots

• To increase the value of the radical

Why is it important to choose the largest perfect square when simplifying radicals?

• To avoid using the factor pairs method

• To increase the index

• To ensure the simplest form

• To minimize the radicand

What is the simplified form of the square root of 160?

• 4√10

• 8√5

• 10√4

• 16√1

What does the factor pairs method involve that the perfect squares method does not?

• Using only prime numbers

• Breaking down the radicand into any factors, not just perfect squares

• Simplifying without doing any calculations

• Ignoring the index

What is the result of simplifying 3√54?

• 9√6

• 18√3

• 6√9

• 3√27