Add ^3√22 + 3√22 + √22

1. 5√22
2. ^3√22 + 4√44
3. 5√66
4. ^3√22 + 4√22

1 answer

The correct answer is option 4. ^3√22 + 4√22.

To solve this expression, note that the terms √22 and ^3√22 have the same radical (√22), so they can be combined.

√22 + ^3√22 = (√22)^1 + (√22)^(1/3) = (√22)^(3/3) + (√22)^(1/3) = (√22)^4/3 + (√22)^1/3 = (√22)^((4+1)/3) = (√22)^(5/3).

Therefore, ^3√22 + 4√22 = (√22)^(5/3) + 4(√22).

This expression cannot be simplified further, so the correct answer is option 4.