Simplifying and Adding Radicals

The video tutorial explains how to add and subtract radicals, focusing on ensuring that both the indices and radicands are the same. It demonstrates simplifying radicals using prime factorization and shows how to add or subtract the coefficients of like radicals.

What must be true for two radicals to be added or subtracted?

• Their radicands must be prime numbers.

• They must both be square roots.

• Their indices and radicands must be the same.

• Their coefficients must be equal.

What is the first step in simplifying the radical 3√54?

• Multiply 54 by 3.

• Find the square root of 54.

• Add 3 to 54.

• Perform the prime factorization of 54.

After simplifying 3√54, what is the new expression?

• 3√9

• 6√3

• 9√6

• 3√6

When adding radicals, what do you do with the coefficients?

• Add them.

• Subtract them.

• Divide them.

• Multiply them.

In the subtraction example, what happens to the coefficients of the radicals?

• They are added.

• They are multiplied.

• They remain unchanged.

• They are subtracted.

What is the result of subtracting 3√3 from 3√3?

• 1

• 6√3

• 0

• 3√3

Why is it important to have the same indices when adding or subtracting radicals?

• To simplify the process of finding the square root.

• To allow the coefficients to be added or subtracted.

• To make sure the radicands can be added.

• To ensure the coefficients can be multiplied.

What should be done if the radicands are not equal when adding radicals?

• Ignore the radicands.

• Change the indices.

• Add the coefficients anyway.

• Simplify the radicands to make them equal.