While reviewing, I remembered the importance of restrictions, something that I had to relearn and remember for the coming up midterm.

A restriction makes sure only certain numbers can replace x in a radical so that the radical still works.

For this radical, ∛×, because the radical index is 3 and not a factor of 2, the restriction will always be x∈R x is the element of the real numbers. This is because no matter if the number is positive or negative, it is to the power of 3, it will solve to be positive.

For numbers in square roots and roots with the index like 4, 6, 8, 10, etc, the numbers must be greater than 0 so that they can solve.

√x, x≥0

if there are more numbers under the radical, we solve the inequality.

√(x+5)

x+5 ≥ 0

-5

x ≥ -5

That is how restrictions are found. It is important that restrictions are always shown and matched up with the answers of x to make sure x truly follows its restriction.