Product Property of Radicals

The video tutorial covers the properties of radicals, focusing on the product property. It explains the simplest form of radical expressions and highlights illegal algebraic moves, such as adding radicals directly. The tutorial demonstrates the product property, showing that multiplying radicands and taking the square root is valid. It provides examples of simplifying radical expressions and algebraic expressions with radicals, emphasizing the importance of identifying perfect squares and using prime factorization.

What is a condition for a radical expression to be in its simplest form?

• The radicand must be a prime number.

• The radicand must not contain fractions.

• The radicand must be greater than 100.

• The radicand must be an even number.

Which of the following is a valid operation with radicals?

• Dividing two radicals directly.

• Subtracting two radicals directly.

• Multiplying two radicals and then taking the square root.

• Adding two radicals directly.

What is the product property of square roots?

• The square root of a sum is the sum of the square roots.

• The square root of a product is the product of the square roots.

• The square root of a difference is the difference of the square roots.

• The square root of a quotient is the quotient of the square roots.

How can the square root of 245 be simplified?

• As 5 times the square root of 7.

• As 49 times the square root of 5.

• As 7 times the square root of 5.

• As 5 times the square root of 49.

What is the simplified form of the expression 2x times the square root of x?

• 2 times the square root of x squared.

• 2x squared times the square root of x.

• 2x times the square root of x.

• x times the square root of 2x.

How is the square root of 18 simplified?

• As 3 times the square root of 2.

• As 2 times the square root of 9.

• As 9 times the square root of 2.

• As 2 times the square root of 3.

What is the simplified form of the square root of 50 times b to the fifth?

• 5b times the square root of 2b squared.

• 5b squared times the square root of 2b.

• 5b squared times the square root of 5b.

• 5b times the square root of 10b.