Adding and Simplifying Radicals

This video tutorial covers the process of adding and subtracting radical expressions, focusing on like radicals. It explains the criteria for like radicals, which include having the same index and radicand, and provides guidelines for simplifying and combining them. The tutorial includes several examples, demonstrating how to simplify radicals, factor out common terms, and rationalize denominators before performing addition or subtraction. The video emphasizes the importance of simplifying radicals first, similar to combining like terms in algebra.

What are like radicals?

• Radicals with different coefficients

• Radicals that cannot be simplified

• Radicals with the same index and radicand

• Radicals with different indices and radicands

How do you add like radicals?

• By multiplying the radicands

• By subtracting the coefficients

• By adding the indices

• By adding the coefficients

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

• 9√5

• 6√5

• 7√5

• 5√5

What must be done before adding radicals with different radicands?

• Simplify the radicals

• Subtract the coefficients

• Add the indices

• Multiply the radicands

What is the simplified form of √75?

• √15

• 15√3

• 3√5

• 5√3

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

• 14x²√6x

• 8x²√6x

• 10x²√6x

• 12x²√6x

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

• 14x²√6x

• 16x²√6x

• 18x²√6x

• 20x²√6x

How do you eliminate the square root from the denominator?

• Subtract the square root from the numerator

• Multiply the numerator and denominator by the square root

• Divide the numerator by the square root

• Add the square root to the numerator

What is the common denominator used in the final example?

• 6

• 3

• 4

• 5

What is the final result of the expression involving √30 in the last example?

• 2√30/5

• 3√30/5

• 5√30/6

• 5√30/3