Simplifying Radicals and Exponents

The video tutorial from moomoomath explains how to simplify radicals with variables. It begins with an example involving the square root of 49e^12f^7, demonstrating how to factor and simplify by taking out like terms. The process involves identifying pairs of variables and simplifying the expression to 42e^5f^3√f. The tutorial then covers a more complex example with a fourth root, breaking down the number 32 and variables x^8 and y to simplify the expression to 2x^2√(2y). The video aims to help viewers understand the process of simplifying radicals with variables and different roots.

What is the first step in simplifying a radical expression with variables?

• Add all the numbers under the radical.

• Divide the numbers under the radical by 2.

• Look for like factors to take out of the radical.

• Multiply all the numbers under the radical.

What is the result of factoring 49 in the context of simplifying radicals?

• 49 is factored into 5 times 9.

• 49 is factored into 7 times 7, a perfect square.

• 49 is factored into 6 times 8.

• 49 is a prime number.

How many pairs of e's are there in e^10?

• 6 pairs

• 3 pairs

• 4 pairs

• 5 pairs

What do you do with the leftover f when simplifying f^7?

• Ignore it.

• Multiply it by 2.

• Leave it under the radical.

• Add it to the outside of the radical.

What is the first step in solving a problem with a fourth root?

• Look for groups of 2.

• Look for groups of 3.

• Look for groups of 4.

• Look for groups of 5.

How is the number 32 broken down in the context of simplifying radicals?

• 32 is broken down into 8 times 4.

• 32 is broken down into 5 times 6.

• 32 is broken down into 10 times 3.

• 32 is broken down into 2 times 16, and 16 into 4 times 4.

How many groups of 4 are there in x^8?

• 4 groups

• 1 group

• 2 groups

• 3 groups

What happens to a single y in the context of a fourth root problem?

• It is taken out of the radical.

• It is ignored.

• It is left under the radical.

• It is multiplied by 2.

What is the final expression for the second problem involving a fourth root?

• 2x^2 fourth root of 2y

• 2x^2 fourth root of y

• x^2 fourth root of 2y

• 2x fourth root of 2y