Use the properties of radicals to simplify each expression.

Question

1.³√2³√32

2.⁴√2⁴√8

3.√50/√2



4.2/3 - √5

Answer 1

1, ³√2³√32 = ³√64 = ³√4³ = 4

2. ⁴√2⁴√8 = ⁴√16 = ⁴√2⁴ = 2

3. √50/√2 = √100 = √10² = 10

4. 2/3 - √5 This is already simplified although, you COULD combine them together into a single rational expression by getting a common denominator:

I'm wondering if this last problem should have been written as 2/(3 - √5)

If so, you would multiply both numerator and denominator by the conjugate of the denominator.

Answer 2

1. cube root (2) * cube root (32) = cube root (2 * 32) = cube root(64) = 4
2. 4th root (2) * 4th root (8) = 4th root (2 * 8) = 4th root (16) = 2
3. sqrt(50) * sqrt(2) = sqrt(50 * 2) = sqrt (100) = 10
4. not sure what can be done with this as expressed