Exploring Operations with Radicals

This video tutorial covers operations with radicals, focusing primarily on square roots. It begins with an introduction to simplifying radicals and combining like terms. The tutorial then explores adding and subtracting radicals, emphasizing the importance of treating radicals like variables. It progresses to multiplying radicals, including distributing and foiling techniques. The video concludes with advanced examples, demonstrating how to handle complex radical expressions and simplify them effectively.

What is the first step when adding or subtracting radicals?

• Simplify each radical

• Multiply the coefficients

• Combine like terms

• Divide the radicals

If you have 3√5 + 7√5, what is the result?

• 21√5

• 10√5

• 3√12

• 10√10

What is the result of 3√5 - 7√5?

• 10√5

• -4√5

• -10√5

• 4√5

How do you simplify √12?

• 2√3

• 6√2

• 3√2

• 4√3

What is the result of combining 7√2 - 6√2 + 4√2?

• 2√2

• 15√2

• 3√2

• 5√2

When multiplying radicals, what should you do first?

• Multiply the numbers inside the radicals

• Subtract the radicals

• Multiply the coefficients outside the radicals

• Add the radicals

What is the result of multiplying 2√3 and -5√7?

• 10√10

• -10√21

• 10√21

• -10√10

How do you simplify √20?

• 5√2

• 4√5

• 2√5

• 2√10

What is the result of (4 + √6)²?

• 16 + 4√6 + 36

• 16 + 8√6 + 6

• 16 + 4√6 + 6

• 16 + 8√6 + 36

What is the simplified form of 3(√5)²?

• 9√5

• 15

• 3√25

• 3√10