Multiplying Radicals and Conjugates

This video tutorial covers the multiplication of radical expressions, starting with basic principles and moving through several examples. It explains how to multiply coefficients and radicands, simplify expressions, and handle more complex cases. The video also introduces the concept of conjugates, demonstrating their properties and how they simplify radical expressions. The tutorial concludes with examples of multiplying conjugates and highlights the elimination of square roots in the process.

What is the first step in multiplying two radicals with the same index?

• Subtract the radicands

• Divide the radicands

• Add the coefficients

• Multiply the coefficients

When multiplying radicals, what should you do after multiplying the radicands?

• Add the radicands

• Divide the coefficients

• Subtract the coefficients

• Simplify the expression

In the example of multiplying square roots of 75 and 6, what is the simplified form?

• 25 square root 4

• 20 square root 5

• 10 square root 3

• 15 square root 2

What is the result of multiplying the coefficients 4x and 3 in the given example?

• 15x

• 7x

• 12x

• 10x

How do you express x to the 8th power when the index is 2?

• x to the 3rd times x to the 3rd

• x to the 2nd times x to the 2nd times x to the 2nd times x to the 2nd

• x to the 5th

• x to the 4th

What are conjugates in the context of radical expressions?

• Expressions with different terms and signs

• Expressions with the same terms and signs

• Expressions with the same terms but opposite signs

• Expressions with different terms but same signs

What is the product of two conjugates?

• Product of two squares

• Difference of two squares

• Sum of two squares

• Quotient of two squares

When multiplying conjugates, what happens to the middle terms?

• They are multiplied

• They are subtracted

• They cancel each other out

• They are added

What is the simplified result of multiplying 2 square root of 7 by itself?

• 2 square root of 49

• 2 square root of 21

• 4 square root of 21

• 4 square root of 49

What pattern is observed when multiplying conjugates?

• The first term is the sum of the squares

• The first term is the difference of the squares

• The first term is the square of the first term minus the square of the second term

• The first term is the product of the squares