Simplifying Radical Expressions and Roots

This video tutorial covers the process of simplifying radical expressions, focusing on radicals without fractions, using prime factorization, and handling variables with absolute values. It provides examples of simplifying square and cube roots and addresses radicals containing fractions. The tutorial emphasizes the importance of removing perfect nth root factors and ensuring no radicals remain in the denominator of fractions.

What is a radical expression not considered simplified?

• When it contains a fraction

• When it has perfect nth root factors

• When it is a whole number

• When it is a decimal

What is the first step in simplifying a radical expression?

• Add the index to the radicand

• Write the prime factorization of the radicand

• Multiply by the radicand

• Divide by the index

When simplifying the square root of 50, what is the simplified form?

• 5√2

• 10

• √25

• 2√5

What is the cube root of 64?

• 2

• 4

• 8

• 16

When simplifying radicals with variables, when is an absolute value necessary?

• When the index is odd

• When the index is even and the exponent is odd

• When the radicand is negative

• When the radicand is a fraction

In the expression √(8x^4y^7), what is the simplified form?

• 4x^2y^3√(2y)

• 2x^2y^3

• 2x^2y^3√(2y)

• x^2y^3√(2y)

What must be true for a radical expression to be in simplified form?

• All possible nth powered factors must be removed

• It must have a radical in the denominator

• It must be a whole number

• It must have a fraction

How can you simplify a radical expression with a fraction in the denominator?

• Multiply the numerator by the denominator

• Add the same radical to both numerator and denominator

• Multiply both numerator and denominator by a radical that will eliminate the radical in the denominator

• Divide the numerator by the denominator

What is the simplified form of the expression √(9/25)?

• 5/3

• 9/25

• 3/5

• √9/√25

When simplifying the cube root of 2/3, what is the simplified form?

• Cube root of 6

• Cube root of 18

• Cube root of 2

• Cube root of 3