Mastering Addition and Subtraction of Radicals

The video tutorial covers the process of adding and subtracting radical expressions, focusing on like radicals. It explains that like radicals have the same index and radicand, allowing for operations by combining coefficients. The tutorial provides guidelines for simplifying radicals, identifying like radicals, and performing operations. Several examples demonstrate these concepts, including simplifying complex radicals and rationalizing denominators. The video emphasizes the importance of simplifying radicals before combining them, drawing parallels to combining like terms in algebra.

What are like radicals?

• Radicals with different indices and different radicands

• Radicals with the same index and the same radicand

• Radicals with different indices and the same radicand

• Radicals with the same index and different radicands

What is the first step in adding or subtracting radical expressions?

• Add or subtract the coefficients

• Simplify each radical

• Combine the radicands

• Identify the like radicals

In the first example, what is the result of adding 4√5 and 3√5?

• 9√5

• 5√5

• 7√5

• 12√5

Why do we need to simplify radicals before adding or subtracting them?

• To change the index

• To ensure the radicands are the same

• To find perfect square factors

• To make the coefficients equal

What is the simplified form of √75?

• -15√3

• 15√3

• 3√5

• 5√3

In the third example, what is the simplified form of 4x√54?

• 12x²√6x

• 6x²√6x

• 5x√6x

• 18x²√6x

What is the result of adding 12x²√6x and 6x²√6x?

• 18x²√6x

• 12x²√6x

• 24x²√6x

• 6x²√6x

What is the first step in simplifying radicals in fractions?

• Subtract the denominators

• Add the numerators

• Multiply numerator and denominator by the same radical

• Find a common denominator

What is the simplified form of √15/√2?

• √15/3

• √15/2

• √30/3

• √30/2

What is the final result of adding √15/√2 and √10/√3?

• 3√30/6

• 2√30/6

• 5√30/3

• 5√30/6