Exploring Operations with Radicals

This video tutorial covers the basics of adding, subtracting, and multiplying radicals. It explains the importance of having the same root and radicand for addition and subtraction, and demonstrates how to simplify radicals by breaking them down into pairs. The tutorial also covers the multiplication of radicals, emphasizing the process of multiplying outside and inside numbers separately. Several examples are provided to illustrate these concepts, including more complex problems that require distribution and further simplification.

What must be the same in order to add or subtract radicals?

• The root and radicand

• The exponents

• The variables

• The coefficients

If you have 1√5 + 2√5, what is the result?

• 1√10

• 3√10

• 3√5

• 2√5

How can √18 be simplified?

• 3√2

• 2√9

• √36

• √9

What is the result of 12√2 - 1√2?

• 13√2

• 10√2

• 11√2

• 11√4

What is the simplified form of 10√3 + 6√3?

• 16√6

• 16√3

• 6√3

• 10√9

When multiplying radicals, what should you multiply together?

• The exponents

• Only the coefficients

• Only the radicands

• Outside numbers with outside numbers and inside numbers with inside numbers

What is the result of 2√5 * 3√10?

• 6√50

• 5√30

• 6√15

• 30√2

What is the simplified form of 2√3 * 2√10?

• 4√30

• 2√30

• 2√13

• 4√13

What is the simplified form of √50?

• 10√5

• √25

• 2√5

• 5√2

What is the result of 2√3 + 2√10 + √15 + 5√2?

• 2√3 + 2√10 + 15 + 5√2

• 2√3 + 2√10 + √15 + 5√2

• 2√3 + 2√10 + √15 + 2√5

• 9√30