Multiplying and Simplifying Radicals

The video tutorial explains how to multiply radical expressions by demonstrating three examples. It covers the multiplication of radicands, prime factorization, and simplification of radicals, including those with variables. The tutorial emphasizes identifying perfect square factors to simplify expressions effectively.

What is the result of multiplying two radicals with the same index?

• The sum of the radicands

• The product of the radicands

• The difference of the radicands

• The quotient of the radicands

What is the prime factorization of 21?

• 2 x 11

• 3 x 7

• 6 x 3

• 5 x 4

Which of the following is a perfect square factor of 21 x 35?

• 3 x 3

• 5 x 5

• 7 x 7

• 2 x 2

How do you multiply radicals with coefficients?

• Multiply the coefficients and add the radicands

• Add the coefficients and multiply the radicands

• Divide the coefficients and multiply the radicands

• Multiply the coefficients and multiply the radicands

What is the prime factorization of 75?

• 3 x 25

• 5 x 15

• 3 x 5 x 5

• 2 x 5 x 5

What is the simplified form of 3√15 * -4√75?

• 180√15

• -180√15

• 180√5

• -180√5

What is the result of multiplying √18x^3 and √10x^2?

• √180x^5

• √180x^6

• √28x^6

• √28x^5

Which of the following is a perfect square factor of x^5?

• x^3

• x^5

• x^2

• x^4

What is the simplified form of the expression involving √18x^3 and √10x^2?

• 5x^3√6x

• 6x^2√5x

• 6x^3√5x

• 5x^2√6x

Why is no absolute value required in the final result?

• Because the radicand is positive

• Because the exponent on x is odd

• Because the exponent on x is even

• Because the radicand is negative