Add ^3√22 + 3√22 + √22
1. 5√22
2. ^3√22 + 4√44
3. 5√66
4. ^3√22 + 4√22
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.
To simplify the expression ^3√22 + 3√22 + √22, you can combine the like terms:
^3√22 + 3√22 + √22
= (^3 + 3 + 1)√22
= ^3√22 + 3√22 + √22
= 7√22
Therefore, the simplified expression is 7√22.
So the correct answer is 7√22, none of the given options are correct.
To simplify the expression ^3√22 + 3√22 + √22, you can combine the like terms.
Step 1: Notice that all terms have √22 in common. So, we can factor out √22.
√22 (^3√1 + 3√1 + 1)
Step 2: Simplify the cube root (^3√1) and the square root (√1).
√22 (1 + 3 + 1)
Step 3: Add the numbers inside the parentheses.
√22 (5)
So, the simplified expression is 5√22.
Therefore, the correct answer is option 1: 5√22.