^3√22 + 3√22 + √22
options are:
^3√22 + 4√22
5√66
5√22
^3√22 + 4√44
^3√22 + 3√22 + √22 can be simplified as follows:
^3√22 + 3√22 + √22 = (1 + 3 + 1)√22 = 5√22
Therefore, the correct option is 5√22.
To simplify the expression ^3√22 + 3√22 + √22, we need to combine the like terms. The like terms in this case are the terms with the same radical (√22).
^3√22 can be written as √(22^(1/3)).
So, rewriting the expression, we get:
√(22^(1/3)) + 3√22 + √22
Now, let's simplify each term individually:
1. √(22^(1/3)) cannot be simplified any further because 22^(1/3) is not a perfect cube.
2. 3√22 cannot be simplified because 22 is not a perfect square.
3. √22 cannot be simplified any further because 22 is not a perfect square.
Combining the terms, we get:
√(22^(1/3)) + 3√22 + √22
Since there are no like terms, we can't combine the terms any further.
Therefore, the simplified expression is √(22^(1/3)) + 3√22 + √22.
To simplify the expression ^3√22 + 3√22 + √22, we can notice that all terms have the same radicand, which is 22.
The first step is to combine like terms. So, ^3√22 + 3√22 can be combined as 4√22.
Now the expression becomes 4√22 + √22.
Next, we can simplify by combining these two terms. Since they have the same radicand, we can add the coefficients in front of the square root, which gives us 4 + 1 = 5.
Thus, the final simplified expression is 5√22.
Comparing this answer with the options provided, we can conclude that the correct answer is 5√22.