Radical Expressions and Simplification

The video tutorial explains how to determine the sum of radical expressions by identifying and simplifying like radicals. It covers the simplification of square roots and cube roots, emphasizing the importance of having the same index and radicand for like radicals. The tutorial provides step-by-step examples, including the simplification of square roots of 18 and 50, and cube roots of expressions involving variables. The process involves identifying perfect square and cube factors, simplifying the radicals, and then adding the like radicals.

What is required for radical expressions to be added together?

• They must be positive.

• They must have the same coefficients.

• They must have like radicals.

• They must be in decimal form.

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

• Divide the number by 2.

• Convert to a fraction.

• Find the prime factorization.

• Multiply by 10.

Which of the following is a perfect square factor of 18?

• 6

• 9

• 3

• 2

How do you add like radicals?

• By dividing the radicands.

• By multiplying the radicands.

• By adding the coefficients.

• By subtracting the indices.

What is the simplified form of 6√2 + 5√2?

• 1√2

• 60√2

• 11√2

• 30√2

What is the first step in simplifying cube roots?

• Convert to a decimal.

• Multiply by 3.

• Identify perfect cube factors.

• Find the square root.

Which of the following is a perfect cube factor of y^5?

• y^2

• y^5

• y^3

• y^4

What is the simplified form of x * the cube root of x^2 y^5?

• x^2 * the cube root of y^5

• y * the cube root of x^2 y^5

• x * the cube root of x^2 y^2

• x * y * the cube root of x^2 y^2

How do you add like radicals with cube roots?

• By subtracting the indices.

• By adding the coefficients.

• By multiplying the radicands.

• By dividing the radicands.

What is the sum of x * the cube root of x^2 y^5 and y * the cube root of x^5 y^2?

• x * y * the cube root of x^2 y^2

• 2xy * the cube root of x^2 y^2

• xy * the cube root of x^5 y^5

• x^2 * y^2 * the cube root of x^2 y^2