Simplifying Radical Expressions and Factoring

This video tutorial covers the multiplication of radical expressions, starting with basic examples and progressing to more complex scenarios involving cube and fourth roots, as well as variables. The tutorial emphasizes the importance of simplifying expressions before multiplying, especially when dealing with large numbers. It also includes a section on factoring and simplifying trinomials, providing a comprehensive overview of handling radicals in mathematical expressions.

What is the result of multiplying the square root of 3 by the square root of 5?

• Root 30

• Root 15

• Root 8

• Root 10

When multiplying the square root of 6 by the square root of 15, what is the simplified form?

• Root 45

• 6 root 5

• Root 90

• 3 root 10

Why is it sometimes better to simplify before multiplying radical expressions?

• It is a rule of mathematics

• It is always faster

• It reduces the complexity of calculations

• It makes the numbers larger

What is the simplified form of the square root of 10 times the square root of 35?

• 10 root 7

• 5 root 14

• Root 350

• Root 70

How do you simplify the cube root of 18 times the cube root of 6?

• 6 cube root of 3

• 2 cube root of 9

• Cube root of 108

• 3 cube root of 4

What is the result of multiplying the square root of 18x^3 by the square root of 72x^5?

• 72x^8

• 54x^4

• 18x^8

• 36x^4

In the expression involving the cube root of 12x^5y^3 times the cube root of 6x^8y^7, what is the simplified form?

• x^4y^3 cube root of 18xy

• 3x^4y^3 cube root of 6xy

• 2x^4y^3 cube root of 9xy

• 2x^3y^2 cube root of 9xy

What is the simplified form of the fourth root of 18a^11b^15 times the fourth root of 27a^13b^9?

• a^6b^6 fourth root of 54

• 3a^6b^6 fourth root of 6

• 3a^5b^5 fourth root of 6

• 2a^6b^6 fourth root of 9

How can you factor the expression x^2 + 6x + 9?

• (x + 3)(x + 3)

• (x + 2)(x + 4)

• (x + 1)(x + 9)

• (x + 3)(x + 6)

What is the simplified form of the square root of (x + 3)^2?

• x^2 + 9

• x^2 + 6x + 9

• x + 3

• x + 6