Simplifying and Adding Radicals

The video tutorial explains how to add and subtract terms containing radicals. It emphasizes that the radical factors must be identical to perform these operations. The tutorial provides examples to demonstrate the process, including simplifying radicals, identifying like radicals, and adding or subtracting their coefficients. It also covers handling coefficients in radical expressions and dealing with complex expressions involving multiple radicals. The lesson concludes with a summary and a preview of upcoming topics.

What must be true for two radicals to be added or subtracted?

• They must have the same coefficients.

• They must have the same radical factors.

• They must be integers.

• They must be perfect squares.

What is the first step in adding or subtracting radicals?

• Divide the coefficients.

• Multiply the radicands.

• Simplify each radical.

• Add the coefficients.

In the expression 7√5 - 3√5, what is the result?

• 10√5

• 4√5

• 4√10

• 7√2

What is the purpose of factoring out a common radical factor?

• To simplify the expression by combining like terms.

• To increase the coefficient.

• To change the radicand.

• To eliminate the radical.

If you have √m + 13√m, what is the simplified form?

• 14√m

• 13√m

• √m

• 14m

What is the coefficient of the first term in √m + 13√m?

• 1

• 0

• 13

• 14

In the expression 4√10 - 19√10 + 7√10, what is the final result?

• 12√10

• 0

• -8√10

• 8√10

What remains unchanged when adding or subtracting like radicals?

• The entire expression

• The radical part

• The numerical value

• The coefficients

Why is it important to simplify radicals before adding or subtracting?

• To change the index of the radical.

• To eliminate the radical.

• To make sure the radicands are the same.

• To ensure the coefficients are integers.

What is the result of 4 - 19 + 7 in the context of radicals?

• 12

• 0

• 8

• -8