Exploring Adding and Subtracting Radicals

The video tutorial covers radical rules, starting with the conjugate root theorem to rationalize expressions. It explains how to multiply by conjugates to eliminate radicals in denominators. The tutorial also discusses adding and subtracting radicals, emphasizing the need for matching indices and radicands. Simplification techniques are demonstrated, including prime factorization and combining like terms. The video aims to reinforce prior knowledge and introduce new concepts related to radicals.

What is the conjugate of the expression 1 - √2?

• -1 - √2

• 1 + √2

• 1 - √2

• -1 + √2

Why do we use the conjugate root theorem?

• To simplify the numerator

• To add radicals

• To get an integer result

• To subtract radicals

When rationalizing a fraction, what must you multiply the numerator and denominator by?

• The original denominator

• The conjugate of the numerator

• The conjugate of the denominator

• The original numerator

What is the simplified form of 8√8?

• 2√2

• 8√2

• 16√2

• 4√2

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

• They must be in the denominator

• They must be in the numerator

• They must have the same index and radicand

• They must have the same coefficient

What is the first step in simplifying radicals for addition or subtraction?

• Multiplying by the conjugate

• Prime factorization

• Dividing by the radicand

• Combining like terms

How is 20 written in prime factorization form?

• 2^2 * 5

• 2^3 * 5

• 2^2 * 3

• 2^3 * 3

What is the simplified form of 28√5 - 15√5?

• 43√10

• 13√10

• 43√5

• 13√5

What should you do if the roots in an expression do not match?

• Simplify the radicals first

• Subtract them anyway

• Multiply them

• Add them anyway

What is the final simplified form of 6∛2 + 4∛2?

• 12∛2

• 8∛2

• 10∛2

• 2∛2