Exploring Operations with Radicals

This video tutorial covers operations with radical expressions, including addition, subtraction, multiplication, and division. It explains the importance of having the same index and number inside the radical for addition and subtraction, and demonstrates how to simplify radicals. The tutorial also covers multiplying and dividing radicals, emphasizing the need to multiply outside numbers with outside numbers and inside numbers with inside numbers. The video concludes with a discussion on using conjugates to eliminate radicals from denominators.

What must be true for two radical expressions to be added or subtracted?

• They must have different numbers inside the radical.

• They must have the same index and the same number inside the radical.

• They must have the same coefficients.

• They must have different indices.

If you have 6√3 + 13√3, what is the result?

• 19√3

• 6√3

• 19√6

• 13√3

How do you simplify the expression 6√3 + 5√12?

• 6√3 + 10√3

• 6√3 + 5√12

• 11√3

• 16√3

What is the simplified form of 8√5 - 3√45 - 4√80?

• √5

• 5√5

• 8√5 - 3√5 - 4√5

• 1√5

When multiplying radical expressions, what must be true?

• The numbers inside the radicals must be the same.

• You can multiply any radicals regardless of their indices.

• You can multiply outside numbers with outside numbers and inside numbers with inside numbers.

• The numbers outside the radicals must be the same.

What is the result of multiplying 3√3 * 5√3?

• 45

• 15√9

• 15√6

• 15√3

How do you simplify the expression 2√5 * 12√8?

• 24√40

• 48√10

• 24√10

• 48√40

What is the first step in dividing radical expressions?

• Multiply the radicals together.

• Subtract the radicals.

• Add the radicals together.

• Multiply the numerator and denominator by the same radical.

How do you rationalize the denominator of 6√3 / √9?

• Multiply by 3

• Multiply by 6

• Multiply by √9

• Multiply by √3

What is the purpose of using the conjugate in radical expressions?

• To eliminate the radical in the denominator.

• To add radicals together.

• To multiply radicals together.

• To simplify the numerator.