Exploring Adding and Subtracting Radicals

What must be true about radicals in order to add or subtract them?

• They must be whole numbers.

• They must be prime numbers.

• They must have the same index and radicand.

• They must have the same coefficient.

In the expression 8√7 + 5√7, what is the result?

• 40√7

• 13√14

• 3√7

• 13√7

How do you handle a radical without a written coefficient?

• Assume the coefficient is negative one.

• Assume the coefficient is ten.

• Assume the coefficient is one.

• Assume the coefficient is zero.

What is the result of 3√11 + 6√11 - 2√11?

• 9√11

• 7√11

• 1√11

• 11√11

When combining 9√7 + 5√7 - 4√2 + 3√2, what is the simplified form?

• 14√7 - 1√2

• 14√7 + √2

• 14√7 + 1√2

• 14√7 - √2

What should you do if radicals are not alike from the start?

• Add them directly.

• Subtract them directly.

• Simplify each radical as much as possible.

• Ignore the radicals.

Simplify 3√7 - 2√28. What is the result?

• √28

• √35

• √7

• √49

What is the simplified form of 49√2 + 20√2 - 10√3?

• 69√2 + √3

• 69√2 + 10√3

• 69√2 - √3

• 69√2 - 10√3

How do you simplify 27√x?

• 9√3x

• 3√9x

• √27x

• √3x

What is the result of combining 9√3 + 20√3?

• 29√3

• 39√3

• 11√3

• 19√3