Add ^3√22 + 3√22 + √22.

Answer 1

^3√22 + 3√22 + √22 can be simplified as follows:

^3√22 is the same as 22^(1/3).
3√22 is the same as 3 * 22^(1/2).
√22 is the same as 1 * 22^(1/2).

To add these terms, we need to have the same exponent for the base 22. Since ^3√22 has an exponent of 1/3, we need to convert the other terms to the same exponent. We can do this by rewriting 22^(1/2) as 22^(2/6) and 22^(1/3) as 22^(2/6).

So, ^3√22 + 3√22 + √22 becomes:
22^(1/3) + 3 * 22^(2/6) + 1 * 22^(2/6).

Now that they share the same exponent, we can add the coefficients of the terms:
1/3 + 3 * 2/6 + 2/6.

Simplifying the coefficients, we get:
1/3 + 1 + 1/3.

Combining the coefficients, we have:
1/3 + 3/3 + 1/3 = 5/3.

Therefore, ^3√22 + 3√22 + √22 equals 5/3.