Simplifying Radicals with Variables

The video tutorial covers simplifying radicals using different methods. It begins with an introduction to simplifying radicals and then demonstrates using factor trees. An alternative method is introduced, followed by a division method for simplifying radicals. The tutorial concludes with examples applying the division method.

What is the first step in simplifying the radical expression 54, x^9, y^5, and w^7?

• Separate the terms into individual radicals

• Add the exponents of the variables

• Multiply all the terms together

• Combine all terms under one radical

When simplifying the cube root of 54, what is the result of the factor tree for 54?

• 9 x 6

• 2 x 27

• 3 x 18

• 6 x 9

How many groups of three x's are there in x^9 when simplifying the cube root?

• 2

• 1

• 3

• 4

What is the simplified form of y^5 under a cube root?

• y^2 under the radical

• y^2

• y^3

• y

In the quicker method, what do you do with the exponent of a variable when dividing by the index of the radical?

• Subtract the index from the exponent

• Add the index to the exponent

• Divide the exponent by the index

• Multiply the exponent by the index

Using the quicker method, what is the simplified form of a^5 under a cube root?

• a^2 under the radical

• a^2

• a^3

• a

What is the simplified form of b^7 under a cube root using the quicker method?

• b^2

• b^3

• b

• b^2 under the radical

In the final example, what is the simplified form of w^5 under a fourth root?

• w

• w^2

• w^3

• w^4

What is the simplified form of x^12 under a fourth root?

• x

• x^4

• x^3

• x^2

What is the simplified form of y^2 under a fourth root?

• y^2 under the radical

• y under the radical

• y

• y^2