Exploring Operations with Radicals

The video tutorial covers simplifying radicals and performing operations such as adding, subtracting, and multiplying them. It explains the rules for adding and subtracting radicals, emphasizing the need for the same index and radicand. Examples are provided to illustrate these operations, including rewriting and simplifying radicals. The tutorial also covers multiplying radicals, focusing on multiplying coefficients and radicands while ensuring the same index. The video concludes with examples of multiplying radicals, highlighting the importance of simplification.

What must be true about the radicals in order to add or subtract them?

• They must be perfect squares.

• They must have the same index and radicand.

• They must be different.

• They must have the same coefficient.

When adding or subtracting radicals, what part of the radicals do you add or subtract?

• The entire radical

• The radicands

• The indices

• The coefficients

In the example of adding radicals, what is the largest perfect square that divides into 200?

• 100

• 50

• 25

• 4

What is the simplified form of 17√8?

• 17√4

• 34√8

• 34√2

• 8√17

In the subtraction example, what is the largest perfect square that divides into 48?

• 16

• 12

• 36

• 4

What is the simplified form of 6√48?

• 24√2

• 6√16

• 18√3

• 24√3

When multiplying radicals, what must be the same?

• The coefficients

• The entire radical

• The radicands

• The indices

What is the simplified form of 5√12 * 2√6?

• 30√6

• 60√12

• 60√2

• 10√18

In the example of multiplying three radicals, what is the coefficient of the final result?

• 6

• 5

• 60

• 12

What is the simplified form of √3 * √5 * √10?

• 60√2

• 12√5

• 60√6

• √150