Simplifying Radicals and Factorization

The video tutorial explains how to simplify radical expressions, focusing on square and cube roots. It begins by discussing the conditions under which a radical expression is considered simplified. The tutorial then provides a step-by-step guide to simplifying the square root of a fraction by identifying perfect square factors. It continues with an example of simplifying a cube root by finding perfect cube factors. The video emphasizes the importance of removing fractions under radicals and radicals in denominators to achieve a simplified form.

What is a condition for a radical expression to be considered simplified?

• It must not have a numerator.

• It must have a radical in the denominator.

• It must have a fraction under the radical.

• It must not have a fraction under the radical.

What is the first step in simplifying the square root of a fraction?

• Add the numerator and denominator.

• Check if the fraction can be simplified.

• Subtract the numerator from the denominator.

• Multiply the numerator and denominator.

What is the perfect square factor of 75?

• 9

• 16

• 25

• 36

How is the square root of 16 expressed using exponents?

• 4^2

• 2^4

• 4^1

• 16^1

What is the simplified form of the square root of 75/16?

• 5√3 / 4

• 3√5 / 4

• 4√5 / 3

• 5√4 / 3

What is the greatest common factor between 324 and 4?

• 8

• 1

• 2

• 4

What is the cube root of 81 simplified to?

• 9

• 3√3

• 27

• 81

What is the prime factorization of 81?

• 2^4

• 3^4

• 9^2

• 4^3

How many equal factors of 3 are in the prime factorization of 81?

• 2

• 3

• 4

• 5

What does the cube root of 3 cubed simplify to?

• 3

• 4

• 1

• 2