Simplifying Radical Expressions in Algebra

This video tutorial introduces algebra students to radical expressions, focusing on simplifying them using the product property of radicals. It covers identifying perfect squares, using prime factorization, and handling expressions with powers of 10 and variables. The tutorial includes practical examples and concludes with an application problem involving the area of a square.

What is a radical expression?

• An expression with a variable.

• An expression with a fraction.

• An expression with a square root symbol.

• An expression with an exponent.

What does simplified radical form mean?

• An expression simplified as much as possible but still containing a square root symbol.

• An expression with only whole numbers.

• An expression with no square root symbol.

• An expression with only variables.

Which of the following is a perfect square number?

• 20

• 25

• 30

• 35

What is the square root of 64?

• 6

• 7

• 9

• 8

According to the product property of radicals, what is the square root of 25 * 3?

• 5 * 3

• sqrt(25 * 3)

• 5 * sqrt(3)

• sqrt(25) * 3

What is the simplified form of the square root of 75?

• 3 * sqrt(5)

• sqrt(75)

• sqrt(25 * 3)

• 5 * sqrt(3)

What is the prime factorization of 363?

• 3 * 121

• 3 * 33

• 3 * 11 * 11

• 11 * 33

What is the simplified form of the square root of 363?

• 3 * sqrt(11)

• 11 * sqrt(3)

• sqrt(3 * 11 * 11)

• sqrt(363)

What is the simplified form of the square root of 90 * b^2 * c^4?

• 3 * b * c^2 * sqrt(10)

• sqrt(90) * b^2 * c^4

• sqrt(9 * 10) * b * c^2

• 3 * sqrt(10) * b * c^2

What is the simplified form of the square root of 25x^3y^7?

• 5xy^3 * sqrt(xy)

• 5x^2y^3 * sqrt(xy)

• 5x^3y^7

• 5xy^3 * sqrt(x^2y)