Simplifying Radicals and Factorization

The video tutorial explains how to simplify radical expressions, focusing on square and cube roots. It covers the importance of removing fractions under radicals and radicals in denominators. The tutorial provides step-by-step instructions for simplifying square roots by identifying perfect square factors and cube roots by finding perfect cube factors. The video concludes with a summary of the key points discussed.

What is a radical expression not considered simplified?

• When it is a whole number

• When it contains a fraction under the radical

• When it has a radical in the numerator

• When it is a perfect square

What is the first step in simplifying the square root of 100x/5x?

• Multiply the numerator and denominator

• Simplify the fraction under the radical

• Add a constant to the expression

• Divide the expression by 2

How can 100x be expressed to simplify the fraction 100x/5x?

• As 10 * 10x

• As 20 * 5x

• As 50 * 2x

• As 25 * 4x

What is the prime factorization of 20?

• 2 * 10

• 2 * 5 * 5

• 4 * 5

• 2 * 2 * 5

What property is used to simplify the cube root of a fraction?

• The quotient property of radicals

• The product property of radicals

• The sum property of radicals

• The difference property of radicals

What is the result of simplifying the fraction 64/4 under a cube root?

• 20

• 16

• 12

• 8

How is y^5/y^2 simplified?

• y^2

• y^0

• y^3

• y^1

What is the prime factorization of 16?

• 2 * 2 * 2 * 2

• 8 * 2

• 4 * 4

• 2 * 4 * 2

What is the cube root of 2 cubed?

• 4

• 3

• 2

• 1

Why is there no need for an absolute value in the final expression?

• Because the index is even

• Because the expression is a whole number

• Because the index is odd

• Because the expression is a fraction